All Stories

  1. Influence of numerical noise on surface quasi-geostrophic turbulence

    Article • Physics of Fluids, March 2025, American Institute of Physics

    Professor Shijun Liao

  2. Accurate predictions of chaotic motion of a free fall disk

    Article • Physics of Fluids, March 2021, American Institute of Physics

    Professor Shijun Liao

  3. Steady-state multiple near resonances of periodic interfacial waves with rigid boundary

    Article • Physics of Fluids, August 2020, American Institute of Physics

    Professor Shijun Liao

  4. On collinear steady-state gravity waves with an infinite number of exact resonances

    Article • Physics of Fluids, December 2019, American Institute of Physics

    Professor Shijun Liao

  5. On the steady-state resonant acoustic–gravity waves

    Article • Journal of Fluid Mechanics, June 2018, Cambridge University Press

    Professor Shijun Liao

  6. On the steady-state nearly resonant waves

    Article • Journal of Fluid Mechanics, March 2016, Cambridge University Press

    Professor Shijun Liao

  7. On the existence of steady-state resonant waves in experiments

    Article • Journal of Fluid Mechanics, December 2014, Cambridge University Press

    Professor Shijun Liao

  8. Observations of highly localized oscillons with multiple crests and troughs

    Article • Physical Review E, September 2014, American Physical Society (APS)

    Professor Shijun Liao

  9. Phase velocity effects of the wave interaction with exponentially sheared current

    Article • Wave Motion, September 2014, Elsevier

    Professor Shijun Liao

  10. A HAM-based analytic approach for physical models with an infinite number of singularities

    Article • Numerical Algorithms, June 2014, Springer Science + Business Media

    Professor Shijun Liao

  11. Steady-state resonance of multiple wave interactions in deep water

    Article • Journal of Fluid Mechanics, February 2014, Cambridge University Press

    Professor Shijun Liao

  12. Advances in the Homotopy Analysis Method

    Article • January 2014, World Scientific Pub Co Pte Lt

    Professor Shijun Liao

  13. Chapter 1: Chance and Challenge: A Brief Review of Homotopy Analysis Method

    Article • December 2013, World Scientific Pub Co Pte Lt

    Professor Shijun Liao

  14. Chapter 9: HAM-Based Mathematica Package BVPh 2.0 for Nonlinear Boundary Value Problems

    Article • December 2013, World Scientific Pub Co Pte Lt

    Professor Shijun Liao

  15. Two new standing solitary waves in shallow water

    Article • Wave Motion, June 2013, Elsevier

    Professor Shijun Liao

  16. On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems

    Article • Chaos Solitons & Fractals, February 2013, Elsevier

    Professor Shijun Liao

  17. On peaked solitary waves of the Degasperis-Procesi equation

    Article • Science China Physics Mechanics and Astronomy, January 2013, Springer Science + Business Media

    Professor Shijun Liao

  18. Two kinds of peaked solitary waves of the KdV, BBM and Boussinesq equations

    Article • Science China Physics Mechanics and Astronomy, November 2012, Springer Science + Business Media

    Professor Shijun Liao

  19. On the steady-state fully resonant progressive waves in water of finite depth

    Article • Journal of Fluid Mechanics, September 2012, Cambridge University Press

    Professor Shijun Liao

  20. Chaos: A bridge from microscopic uncertainty to macroscopic randomness

    Article • Communications in Nonlinear Science and Numerical Simulation, June 2012, Elsevier

    Professor Shijun Liao

  21. A maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations

    Article • Journal of Systems Science and Complexity, June 2012, Springer Science + Business Media

    Professor Shijun Liao

  22. The improved homotopy analysis method for the Thomas–Fermi equation

    Article • Applied Mathematics and Computation, May 2012, Elsevier

    Professor Shijun Liao

  23. Homotopy Analysis Method in Nonlinear Differential Equations

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  24. On the HAM-based mathematica package BVPh for coupled nonlinear ODEs

    Article • January 2012, American Institute of Physics

    Professor Shijun Liao

  25. Introduction

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  26. Relationship to Euler Transform

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  27. Unsteady Boundary-layer Flows

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  28. Mathematica Package BVPh

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  29. Optimal Homotopy Analysis Method

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  30. On the quartet resonance of gravity waves in water of finite depth

    Article • January 2012, American Institute of Physics

    Professor Shijun Liao

  31. Interaction of Nonlinear Water Wave and Nonuniform Currents

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  32. Some Methods Based on the HAM

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  33. Two and Three Dimensional Gelfand Equation

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  34. Nonlinear Boundary-value Problems with Multiple Solutions

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  35. Non-similarity Boundary-layer Flows

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  36. Nonlinear Eigenvalue Equations with Varying Coefficients

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  37. Applications in Finance: American Put Options

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  38. Systematic Descriptions and Related Theorems

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  39. On the dispersion relation of nonlinear wave current interaction by means of the HAM

    Article • January 2012, American Institute of Physics

    Professor Shijun Liao

  40. Resonance of Arbitrary Number of Periodic Traveling Water Waves

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  41. A Boundary-layer Flow with an Infinite Number of Solutions

    Article • January 2012, Springer Science + Business Media

    Professor Shijun Liao

  42. On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves

    Article • Communications in Nonlinear Science and Numerical Simulation, March 2011, Elsevier

    Professor Shijun Liao

  43. Unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet

    Article • Nonlinear Analysis Real World Applications, February 2011, Elsevier

    Professor Shijun Liao

  44. The scaled boundary FEM for nonlinear problems

    Article • Communications in Nonlinear Science and Numerical Simulation, January 2011, Elsevier

    Professor Shijun Liao

  45. Calculation of added mass coefficients of 3D complicated underwater bodies by FMBEM

    Article • Communications in Nonlinear Science and Numerical Simulation, January 2011, Elsevier

    Professor Shijun Liao

  46. EXPLICIT SERIES SOLUTION OF A CLOSURE MODEL FOR THE VON KÁRMÁN–HOWARTH EQUATION

    Article • The ANZIAM Journal, October 2010, Cambridge University Press

    Professor Shijun Liao

  47. An optimal homotopy-analysis approach for strongly nonlinear differential equations

    Article • Communications in Nonlinear Science and Numerical Simulation, August 2010, Elsevier

    Professor Shijun Liao

  48. On the relationship between the homotopy analysis method and Euler transform

    Article • Communications in Nonlinear Science and Numerical Simulation, June 2010, Elsevier

    Professor Shijun Liao

  49. Homotopy based solutions of the Navier–Stokes equations for a porous channel with orthogonally moving walls

    Article • Physics of Fluids, May 2010, American Institute of Physics

    Professor Shijun Liao

  50. An explicit series approximation to the optimal exercise boundary of American put options

    Article • Communications in Nonlinear Science and Numerical Simulation, May 2010, Elsevier

    Professor Shijun Liao

  51. Series solution of non-similarity natural convection boundary-layer flows over permeable vertical surface

    Article • Science China Physics Mechanics and Astronomy, February 2010, Springer Science + Business Media

    Professor Shijun Liao

  52. Series Solution of Non-similarity Boundary-Layer Flows Over a Porous Wedge

    Article • Transport in Porous Media, August 2009, Springer Science + Business Media

    Professor Shijun Liao

  53. On the reliability of computed chaotic solutions of non-linear differential equations

    Article • Tellus A Dynamic Meteorology and Oceanography, August 2009, Co-Action Publishing

    Professor Shijun Liao

  54. Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method

    Article • Nonlinear Analysis Real World Applications, August 2009, Elsevier

    Professor Shijun Liao

  55. SERIES SOLUTION OF LARGE DEFORMATION OF A BEAM WITH ARBITRARY VARIABLE CROSS SECTION UNDER AN AXIAL LOAD

    Article • The ANZIAM Journal, July 2009, Cambridge University Press

    Professor Shijun Liao

  56. An analytical solution for a nonlinear time-delay model in biology

    Article • Communications in Nonlinear Science and Numerical Simulation, July 2009, Elsevier

    Professor Shijun Liao

  57. A general approach to get series solution of non-similarity boundary-layer flows

    Article • Communications in Nonlinear Science and Numerical Simulation, May 2009, Elsevier

    Professor Shijun Liao

  58. Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet

    Article • Computers & Mathematics with Applications, May 2009, Elsevier

    Professor Shijun Liao

  59. Series solutions of non-linear Riccati differential equations with fractional order

    Article • Chaos Solitons & Fractals, April 2009, Elsevier

    Professor Shijun Liao

  60. Analysis of nonlinear fractional partial differential equations with the homotopy analysis method

    Article • Communications in Nonlinear Science and Numerical Simulation, April 2009, Elsevier

    Professor Shijun Liao

  61. On the interaction of deep water waves and exponential shear currents

    Article • Zeitschrift für angewandte Mathematik und Physik, October 2008, Springer Science + Business Media

    Professor Shijun Liao

  62. Series solutions of nano boundary layer flows by means of the homotopy analysis method

    Article • Journal of Mathematical Analysis and Applications, July 2008, Elsevier

    Professor Shijun Liao

  63. Series solutions of unsteady free convection flow in the stagnation-point region of a three-dimensional body

    Article • International Journal of Thermal Sciences, May 2008, Elsevier

    Professor Shijun Liao

  64. A family of new solutions on the wall jet

    Article • European Journal of Mechanics - B/Fluids, May 2008, Elsevier

    Professor Shijun Liao

  65. Dual solutions of boundary layer flow over an upstream moving plate

    Article • Communications in Nonlinear Science and Numerical Simulation, March 2008, Elsevier

    Professor Shijun Liao

  66. A new branch of solutions of boundary-layer flows over a permeable stretching plate

    Article • International Journal of Non-Linear Mechanics, July 2007, Elsevier

    Professor Shijun Liao

  67. A new branch of the temperature distribution of boundary-layer flows over an impermeable stretching plate

    Article • Heat and Mass Transfer, May 2007, Springer Science + Business Media

    Professor Shijun Liao

  68. Newton-homotopy analysis method for nonlinear equations

    Article • Applied Mathematics and Computation, May 2007, Elsevier

    Professor Shijun Liao

  69. A Series Solution of the Unsteady Von Kármán Swirling Viscous Flows

    Article • Acta Applicandae Mathematicae, January 2007, Springer Science + Business Media

    Professor Shijun Liao

  70. Series Solution of Three-Dimensional Unsteady Laminar Viscous Flow Due to a Stretching Surface in a Rotating Fluid

    Article • Journal of Applied Mechanics, January 2007, ASME International

    Professor Shijun Liao

  71. Explicit series solution of travelling waves with a front of Fisher equation

    Article • Chaos Solitons & Fractals, January 2007, Elsevier

    Professor Shijun Liao

  72. Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate

    Article • European Journal of Mechanics - B/Fluids, January 2007, Elsevier

    Professor Shijun Liao

  73. Series solution of unsteady boundary layer flows of non-Newtonian fluids near a forward stagnation point

    Article • Journal of Non-Newtonian Fluid Mechanics, November 2006, Elsevier

    Professor Shijun Liao

  74. Series solutions of unsteady MHD flows above a rotating disk

    Article • Meccanica, October 2006, Springer Science + Business Media

    Professor Shijun Liao

  75. A short communication on Dr. He’s modified Lindstedt–Poincaré method

    Article • Nonlinear Dynamics, September 2006, Springer Science + Business Media

    Professor Shijun Liao

  76. Series Solutions of Unsteady Boundary‐Layer Flows over a Stretching Flat Plate

    Article • Studies in Applied Mathematics, September 2006, Wiley

    Professor Shijun Liao

  77. Finding multiple solutions of nonlinear problems by means of the homotopy analysis method

    Article • Journal of Hydrodynamics, July 2006, Springer Science + Business Media

    Professor Shijun Liao

  78. Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones

    Article • Zeitschrift für angewandte Mathematik und Physik, June 2006, Springer Science + Business Media

    Professor Shijun Liao

  79. An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate

    Article • Communications in Nonlinear Science and Numerical Simulation, June 2006, Elsevier

    Professor Shijun Liao

  80. On the explicit, purely analytic solution of Von Kármán swirling viscous flow

    Article • Communications in Nonlinear Science and Numerical Simulation, February 2006, Elsevier

    Professor Shijun Liao

  81. EXPLICIT ANALYTIC SOLUTIONS OF KDV EQUATION GIVEN BY THE HOMOTOPY ANALYSIS METHOD

    Article • November 2005, World Scientific Pub Co Pte Lt

    Professor Shijun Liao

  82. Comparison between the homotopy analysis method and homotopy perturbation method

    Article • Applied Mathematics and Computation, October 2005, Elsevier

    Professor Shijun Liao

  83. An analytic approach to solve multiple solutions of a strongly nonlinear problem

    Article • Applied Mathematics and Computation, October 2005, Elsevier

    Professor Shijun Liao

  84. Solving solitary waves with discontinuity by means of the homotopy analysis method

    Article • Chaos Solitons & Fractals, October 2005, Elsevier

    Professor Shijun Liao

  85. A challenging nonlinear problem for numerical techniques

    Article • Journal of Computational and Applied Mathematics, September 2005, Elsevier

    Professor Shijun Liao

  86. Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate

    Article • Journal of Non-Newtonian Fluid Mechanics, August 2005, Elsevier

    Professor Shijun Liao

  87. A new branch of solutions of boundary-layer flows over an impermeable stretched plate

    Article • International Journal of Heat and Mass Transfer, June 2005, Elsevier

    Professor Shijun Liao

  88. Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method

    Article • Chaos Solitons & Fractals, March 2005, Elsevier

    Professor Shijun Liao

  89. An analytic approximate approach for free oscillations of self-excited systems

    Article • International Journal of Non-Linear Mechanics, March 2004, Elsevier

    Professor Shijun Liao

  90. On the homotopy analysis method for nonlinear problems

    Article • Applied Mathematics and Computation, January 2004, Elsevier

    Professor Shijun Liao

  91. Beyond Perturbation: Introduction to the Homotopy Analysis Method

    Article • Applied Mechanics Reviews, January 2004, ASME International

    Professor Shijun Liao

  92. Solving high Reynolds-number viscous flows by the general BEM and domain decomposition method

    Article • International Journal for Numerical Methods in Fluids, January 2004, Wiley

    Professor Shijun Liao

  93. Explicit analytic solution for similarity boundary layer equations

    Article • International Journal of Heat and Mass Transfer, January 2004, Elsevier

    Professor Shijun Liao

  94. An explicit analytic solution to the Thomas–Fermi equation

    Article • Applied Mathematics and Computation, December 2003, Elsevier

    Professor Shijun Liao

  95. Beyond Perturbation

    Article • October 2003

    Professor Shijun Liao

  96. An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude

    Article • International Journal of Non-Linear Mechanics, October 2003, Elsevier

    Professor Shijun Liao

  97. A new analytic algorithm of Lane–Emden type equations

    Article • Applied Mathematics and Computation, September 2003, Elsevier

    Professor Shijun Liao

  98. On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet

    Article • Journal of Fluid Mechanics, July 2003, Cambridge University Press

    Professor Shijun Liao

  99. Effects of Nonlinearity and Bottom Friction on Hurricane-Generated Storm Surge in Central Pacific Ocean

    Article • March 2002, American Society of Civil Engineers (ASCE)

    Professor Shijun Liao

  100. Analytic solutions of the temperature distribution in Blasius viscous flow problems

    Article • Journal of Fluid Mechanics, February 2002, Cambridge University Press

    Professor Shijun Liao

  101. A direct boundary element approach for unsteady non-linear heat transfer problems

    Article • Engineering Analysis with Boundary Elements, January 2002, Elsevier

    Professor Shijun Liao

  102. An analytic approximation of the drag coefficient for the viscous flow past a sphere

    Article • International Journal of Non-Linear Mechanics, January 2002, Elsevier

    Professor Shijun Liao

  103. A multigrid approach for steady state laminar viscous flows

    Article • International Journal for Numerical Methods in Fluids, August 2001, Wiley

    Professor Shijun Liao

  104. A non‐iterative numerical approach for two‐dimensional viscous flow problems governed by the Falker–Skan equation

    Article • International Journal for Numerical Methods in Fluids, March 2001, Wiley

    Professor Shijun Liao

  105. A non-iterative numerical approach for two-dimensional viscous flow problems governed by the Falker-Skan equation

    Article • International Journal for Numerical Methods in Fluids, January 2001, Wiley

    Professor Shijun Liao

  106. The general boundary element method and its further generalizations

    Article • International Journal for Numerical Methods in Fluids, October 1999, Wiley

    Professor Shijun Liao

  107. An explicit, totally analytic approximate solution for Blasius’ viscous flow problems

    Article • International Journal of Non-Linear Mechanics, July 1999, Elsevier

    Professor Shijun Liao

  108. A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate

    Article • Journal of Fluid Mechanics, April 1999, Cambridge University Press

    Professor Shijun Liao

  109. GENERAL BOUNDARY-ELEMENT METHOD FOR UNSTEADY NONLINEAR HEAT TRANSFER PROBLEMS

    Article • Numerical Heat Transfer Part B Fundamentals, March 1999, Taylor & Francis

    Professor Shijun Liao

  110. Homotopy analysis method: A new analytic method for nonlinear problems

    Article • Applied Mathematics and Mechanics, October 1998, Springer Science + Business Media

    Professor Shijun Liao

  111. General boundary element method: an application of homotopy analysis method

    Article • Communications in Nonlinear Science and Numerical Simulation, September 1998, Elsevier

    Professor Shijun Liao

  112. An explicit, totally analytic solution of laminar viscous flow over a semi-infinite flat plate

    Article • Communications in Nonlinear Science and Numerical Simulation, June 1998, Elsevier

    Professor Shijun Liao

  113. On the general boundary element method

    Article • Engineering Analysis with Boundary Elements, January 1998, Elsevier

    Professor Shijun Liao

  114. Application of Homotopy Analysis Method in Nonlinear Oscillations

    Article • Journal of Applied Mechanics, January 1998, ASME International

    Professor Shijun Liao

  115. General boundary element method for Poisson equation with spatially varying conductivity

    Article • Engineering Analysis with Boundary Elements, January 1998, Elsevier

    Professor Shijun Liao

  116. On the general Taylor theorem and its applications in solving non-linear problems

    Article • Communications in Nonlinear Science and Numerical Simulation, September 1997, Elsevier

    Professor Shijun Liao

  117. Boundary element method for general nonlinear differential operators

    Article • Engineering Analysis with Boundary Elements, September 1997, Elsevier

    Professor Shijun Liao

  118. A kind of approximate solution technique which does not depend upon small parameters — II. An application in fluid mechanics

    Article • International Journal of Non-Linear Mechanics, September 1997, Elsevier

    Professor Shijun Liao

  119. A kind of direct, implicit numerical scheme for unsteady nonlinear problems

    Article • Communications in Nonlinear Science and Numerical Simulation, September 1997, Elsevier

    Professor Shijun Liao

  120. HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS. PART 2: SOME 2D EXAMPLES

    Article • International Journal for Numerical Methods in Fluids, May 1997, Wiley

    Professor Shijun Liao

  121. HIGH‐ORDER BEM FORMULATIONS FOR STRONGLY NON‐LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON‐LINEAR DIFFERENTIAL OPERATORS. PART 2: SOME 2D EXAMPLES

    Article • International Journal for Numerical Methods in Fluids, May 1997, Wiley

    Professor Shijun Liao

  122. Homotopy analysis method: A new analytical technique for nonlinear problems

    Article • Communications in Nonlinear Science and Numerical Simulation, May 1997, Elsevier

    Professor Shijun Liao

  123. HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS

    Article • International Journal for Numerical Methods in Fluids, October 1996, Wiley

    Professor Shijun Liao

  124. A SHORT NOTE ON HIGH‐ORDER STREAMFUNCTION–VORTICITY FORMULATIONS OF 2D STEADY STATE NAVIER–STOKES EQUATIONS

    Article • International Journal for Numerical Methods in Fluids, January 1996, Wiley

    Professor Shijun Liao

  125. An approximate solution technique not depending on small parameters: A special example

    Article • International Journal of Non-Linear Mechanics, May 1995, Elsevier

    Professor Shijun Liao