Professor Shijun Liao
Shanghai Jiaotong Unicersity
Professor, Mathematics
China, People's Republic of
My Publications
On the steady-state resonant acoustic–gravity waves
Journal of Fluid Mechanics
June 2018
On the steady-state nearly resonant waves
Journal of Fluid Mechanics
March 2016
On the existence of steady-state resonant waves in experiments
Journal of Fluid Mechanics
December 2014
Observations of highly localized oscillons with multiple crests and troughs
Physical Review E
September 2014
Phase velocity effects of the wave interaction with exponentially sheared current
Wave Motion
September 2014
A HAM-based analytic approach for physical models with an infinite number of singularities
Numerical Algorithms
June 2014
Steady-state resonance of multiple wave interactions in deep water
Journal of Fluid Mechanics
February 2014
Advances in the Homotopy Analysis Method
January 2014
Chapter 1: Chance and Challenge: A Brief Review of Homotopy Analysis Method
December 2013
Chapter 9: HAM-Based Mathematica Package BVPh 2.0 for Nonlinear Boundary Value Problems
December 2013
Two new standing solitary waves in shallow water
Wave Motion
June 2013
On the numerical simulation of propagation of micro-level inherent uncertainty for chao...
Chaos Solitons & Fractals
February 2013
On peaked solitary waves of the Degasperis-Procesi equation
Science China Physics Mechanics and Astronomy
January 2013
Two kinds of peaked solitary waves of the KdV, BBM and Boussinesq equations
Science China Physics Mechanics and Astronomy
November 2012
On the steady-state fully resonant progressive waves in water of finite depth
Journal of Fluid Mechanics
September 2012
Chaos: A bridge from microscopic uncertainty to macroscopic randomness
Communications in Nonlinear Science and Numerical Simulation
June 2012
A maple package of automated derivation of homotopy analysis solution for periodic nonl...
Journal of Systems Science and Complexity
June 2012
The improved homotopy analysis method for the Thomas–Fermi equation
Applied Mathematics and Computation
May 2012
Homotopy Analysis Method in Nonlinear Differential Equations
January 2012
On the HAM-based mathematica package BVPh for coupled nonlinear ODEs
January 2012
Introduction
January 2012
Relationship to Euler Transform
January 2012
Unsteady Boundary-layer Flows
January 2012
Mathematica Package BVPh
January 2012
Optimal Homotopy Analysis Method
January 2012
On the quartet resonance of gravity waves in water of finite depth
January 2012
Interaction of Nonlinear Water Wave and Nonuniform Currents
January 2012
Some Methods Based on the HAM
January 2012
Two and Three Dimensional Gelfand Equation
January 2012
Nonlinear Boundary-value Problems with Multiple Solutions
January 2012
Non-similarity Boundary-layer Flows
January 2012
Nonlinear Eigenvalue Equations with Varying Coefficients
January 2012
Applications in Finance: American Put Options
January 2012
Systematic Descriptions and Related Theorems
January 2012
On the dispersion relation of nonlinear wave current interaction by means of the HAM
January 2012
Resonance of Arbitrary Number of Periodic Traveling Water Waves
January 2012
A Boundary-layer Flow with an Infinite Number of Solutions
January 2012
On the homotopy multiple-variable method and its applications in the interactions of no...
Communications in Nonlinear Science and Numerical Simulation
March 2011
Unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat s...
Nonlinear Analysis Real World Applications
February 2011
The scaled boundary FEM for nonlinear problems
Communications in Nonlinear Science and Numerical Simulation
January 2011
Calculation of added mass coefficients of 3D complicated underwater bodies by FMBEM
Communications in Nonlinear Science and Numerical Simulation
January 2011
EXPLICIT SERIES SOLUTION OF A CLOSURE MODEL FOR THE VON KÁRMÁN–HOWARTH EQUATION
The ANZIAM Journal
October 2010
An optimal homotopy-analysis approach for strongly nonlinear differential equations
Communications in Nonlinear Science and Numerical Simulation
August 2010
On the relationship between the homotopy analysis method and Euler transform
Communications in Nonlinear Science and Numerical Simulation
June 2010
Homotopy based solutions of the Navier–Stokes equations for a porous channel with ortho...
Physics of Fluids
May 2010
An explicit series approximation to the optimal exercise boundary of American put options
Communications in Nonlinear Science and Numerical Simulation
May 2010
Series solution of non-similarity natural convection boundary-layer flows over permeabl...
Science China Physics Mechanics and Astronomy
February 2010
Series Solution of Non-similarity Boundary-Layer Flows Over a Porous Wedge
Transport in Porous Media
August 2009
On the reliability of computed chaotic solutions of non-linear differential equations
Tellus A Dynamic Meteorology and Oceanography
August 2009
Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method
Nonlinear Analysis Real World Applications
August 2009
SERIES SOLUTION OF LARGE DEFORMATION OF A BEAM WITH ARBITRARY VARIABLE CROSS SECTION UN...
The ANZIAM Journal
July 2009
An analytical solution for a nonlinear time-delay model in biology
Communications in Nonlinear Science and Numerical Simulation
July 2009
A general approach to get series solution of non-similarity boundary-layer flows
Communications in Nonlinear Science and Numerical Simulation
May 2009
Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a str...
Computers & Mathematics with Applications
May 2009
Series solutions of non-linear Riccati differential equations with fractional order
Chaos Solitons & Fractals
April 2009
Analysis of nonlinear fractional partial differential equations with the homotopy analy...
Communications in Nonlinear Science and Numerical Simulation
April 2009
On the interaction of deep water waves and exponential shear currents
Zeitschrift für angewandte Mathematik und Physik
October 2008
Series solutions of nano boundary layer flows by means of the homotopy analysis method
Journal of Mathematical Analysis and Applications
July 2008
Series solutions of unsteady free convection flow in the stagnation-point region of a t...
International Journal of Thermal Sciences
May 2008
A family of new solutions on the wall jet
European Journal of Mechanics - B/Fluids
May 2008
Dual solutions of boundary layer flow over an upstream moving plate
Communications in Nonlinear Science and Numerical Simulation
March 2008
A new branch of solutions of boundary-layer flows over a permeable stretching plate
International Journal of Non-Linear Mechanics
July 2007
A new branch of the temperature distribution of boundary-layer flows over an impermeabl...
Heat and Mass Transfer
May 2007
Newton-homotopy analysis method for nonlinear equations
Applied Mathematics and Computation
May 2007
A Series Solution of the Unsteady Von Kármán Swirling Viscous Flows
Acta Applicandae Mathematicae
January 2007
Series Solution of Three-Dimensional Unsteady Laminar Viscous Flow Due to a Stretching ...
Journal of Applied Mechanics
January 2007
Explicit series solution of travelling waves with a front of Fisher equation
Chaos Solitons & Fractals
January 2007
Series solutions of unsteady three-dimensional MHD flow and heat transfer in the bounda...
European Journal of Mechanics - B/Fluids
January 2007
Series solution of unsteady boundary layer flows of non-Newtonian fluids near a forward...
Journal of Non-Newtonian Fluid Mechanics
November 2006
Series solutions of unsteady MHD flows above a rotating disk
Meccanica
October 2006
Series Solutions of Unsteady Boundary-Layer Flows over a Stretching Flat Plate
Studies in Applied Mathematics
October 2006
A short communication on Dr. He’s modified Lindstedt–Poincaré method
Nonlinear Dynamics
September 2006
Finding multiple solutions of nonlinear problems by means of the homotopy analysis method
Journal of Hydrodynamics
July 2006
Exponentially decaying boundary layers as limiting cases of families of algebraically d...
Zeitschrift für angewandte Mathematik und Physik
June 2006
An analytic solution of unsteady boundary-layer flows caused by an impulsively stretchi...
Communications in Nonlinear Science and Numerical Simulation
June 2006
On the explicit, purely analytic solution of Von Kármán swirling viscous flow
Communications in Nonlinear Science and Numerical Simulation
February 2006
EXPLICIT ANALYTIC SOLUTIONS OF KDV EQUATION GIVEN BY THE HOMOTOPY ANALYSIS METHOD
November 2005
Comparison between the homotopy analysis method and homotopy perturbation method
Applied Mathematics and Computation
October 2005
An analytic approach to solve multiple solutions of a strongly nonlinear problem
Applied Mathematics and Computation
October 2005
Solving solitary waves with discontinuity by means of the homotopy analysis method
Chaos Solitons & Fractals
October 2005
A challenging nonlinear problem for numerical techniques
Journal of Computational and Applied Mathematics
September 2005
Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused b...
Journal of Non-Newtonian Fluid Mechanics
August 2005
A new branch of solutions of boundary-layer flows over an impermeable stretched plate
International Journal of Heat and Mass Transfer
June 2005
Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotop...
Chaos Solitons & Fractals
March 2005
An analytic approximate approach for free oscillations of self-excited systems
International Journal of Non-Linear Mechanics
March 2004
On the homotopy analysis method for nonlinear problems
Applied Mathematics and Computation
January 2004
Beyond Perturbation: Introduction to the Homotopy Analysis Method
Applied Mechanics Reviews
January 2004
Solving high Reynolds-number viscous flows by the general BEM and domain decomposition ...
International Journal for Numerical Methods in Fluids
January 2004
Explicit analytic solution for similarity boundary layer equations
International Journal of Heat and Mass Transfer
January 2004
An explicit analytic solution to the Thomas–Fermi equation
Applied Mathematics and Computation
December 2003
Beyond Perturbation
October 2003
An analytic approximate technique for free oscillations of positively damped systems wi...
International Journal of Non-Linear Mechanics
October 2003
A new analytic algorithm of Lane–Emden type equations
Applied Mathematics and Computation
September 2003
On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a st...
Journal of Fluid Mechanics
July 2003
Effects of Nonlinearity and Bottom Friction on Hurricane-Generated Storm Surge in Centr...
March 2002
Analytic solutions of the temperature distribution in Blasius viscous flow problems
Journal of Fluid Mechanics
February 2002
A direct boundary element approach for unsteady non-linear heat transfer problems
Engineering Analysis with Boundary Elements
January 2002
An analytic approximation of the drag coefficient for the viscous flow past a sphere
International Journal of Non-Linear Mechanics
January 2002
A non‐iterative numerical approach for two‐dimensional viscous flow problems governed b...
International Journal for Numerical Methods in Fluids
March 2001
A multigrid approach for steady state laminar viscous flows
International Journal for Numerical Methods in Fluids
January 2001
A non-iterative numerical approach for two-dimensional viscous flow problems governed b...
International Journal for Numerical Methods in Fluids
January 2001
The general boundary element method and its further generalizations
International Journal for Numerical Methods in Fluids
October 1999
An explicit, totally analytic approximate solution for Blasius’ viscous flow problems
International Journal of Non-Linear Mechanics
July 1999
A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infin...
Journal of Fluid Mechanics
April 1999
GENERAL BOUNDARY-ELEMENT METHOD FOR UNSTEADY NONLINEAR HEAT TRANSFER PROBLEMS
Numerical Heat Transfer Part B Fundamentals
March 1999
Homotopy analysis method: A new analytic method for nonlinear problems
Applied Mathematics and Mechanics
October 1998
General boundary element method: an application of homotopy analysis method
Communications in Nonlinear Science and Numerical Simulation
September 1998
An explicit, totally analytic solution of laminar viscous flow over a semi-infinite fla...
Communications in Nonlinear Science and Numerical Simulation
June 1998
On the general boundary element method
Engineering Analysis with Boundary Elements
January 1998
Application of Homotopy Analysis Method in Nonlinear Oscillations
Journal of Applied Mechanics
January 1998
General boundary element method for Poisson equation with spatially varying conductivity
Engineering Analysis with Boundary Elements
January 1998
On the general Taylor theorem and its applications in solving non-linear problems
Communications in Nonlinear Science and Numerical Simulation
September 1997
Boundary element method for general nonlinear differential operators
Engineering Analysis with Boundary Elements
September 1997
A kind of approximate solution technique which does not depend upon small parameters — ...
International Journal of Non-Linear Mechanics
September 1997
A kind of direct, implicit numerical scheme for unsteady nonlinear problems
Communications in Nonlinear Science and Numerical Simulation
September 1997
HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL ...
International Journal for Numerical Methods in Fluids
May 1997
HIGH‐ORDER BEM FORMULATIONS FOR STRONGLY NON‐LINEAR PROBLEMS GOVERNED BY QUITE GENERAL ...
International Journal for Numerical Methods in Fluids
May 1997
Homotopy analysis method: A new analytical technique for nonlinear problems
Communications in Nonlinear Science and Numerical Simulation
May 1997
HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL ...
International Journal for Numerical Methods in Fluids
October 1996
A SHORT NOTE ON HIGH‐ORDER STREAMFUNCTION–VORTICITY FORMULATIONS OF 2D STEADY STATE NAV...
International Journal for Numerical Methods in Fluids
January 1996
An approximate solution technique not depending on small parameters: A special example
International Journal of Non-Linear Mechanics
May 1995