What is it about?
Herein, we present a solution to a challenging nonlinear ordinary differential equation (ODE) originating from a problem in Physics. We devise successive approximations with increasing accuracy using the asymptotic analysis and the Lambert W function. From the most successful forms, we formulate a relatively simple analytical form that provides a very accurate solution to the differential equation over the wide range considered here. It is found that the result belongs to the class of super long range kink solutions.
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Why is it important?
It shows how to tackle a difficult nonlinear differential equation for which there is no known analytical solution and through a combination of both numerical and computer algebra methods comes very very close at solving the problem.
Perspectives
The effective analytical solution helps in terms of providing a physical picture to the given problem.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: Solution of a Challenging Nonlinear Differential Equation Arising from a Split-Logarithmic Physical Potential, ACM Communications in Computer Algebra, March 2026, ACM (Association for Computing Machinery),
DOI: 10.1145/3860319.3860320.
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