Author:
He Ji-Huan,Ji Fei-Yu,Mohammad-Sedighi Hamid
Abstract
Purpose
The purpose of this paper is to demonstrate that the numerical method is not everything for nonlinear equations. Some properties cannot be revealed numerically; an example is used to elucidate the fact.
Design/methodology/approach
A variational principle is established for the generalized KdV – Burgers equation by the semi-inverse method, and the equation is solved analytically by the exp-function method, and some exact solutions are obtained, including blowup solutions and discontinuous solutions. The solution morphologies are studied by illustrations using different scales.
Findings
Solitary solution is the basic property of nonlinear wave equations. This paper finds some new properties of the KdV–Burgers equation, which have not been reported in open literature and cannot be effectively elucidated by numerical methods. When the solitary solution or the blowup solution is observed on a much small scale, their discontinuous property is first found.
Originality/value
The variational principle can explain the blowup and discontinuous properties of a nonlinear wave equation, and the exp-function method is a good candidate to reveal the solution properties.
Subject
Applied Mathematics,Computer Science Applications,Mechanical Engineering,Mechanics of Materials
Reference40 articles.
1. Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing Kernel algorithm;International Journal of Numerical Methods for Heat and Fluid Flow,2018
2. Numerical study of unsteady flow and heat transfer CNT-based MHD nanofluid with variable viscosity over a permeable shrinking surface;International Journal of Numerical Methods for Heat and Fluid Flow,2019
3. On two-scale dimension and its applications;Thermal Science,2019
4. Numerical analysis of the counter-intuitive dynamic behavior of the elastic-plastic pin-ended beams under impulsive loading with regard to linear hardening effects;Proceedings of the Institution of Mechanical Engineerings, Part C,2018
5. Laplace transform: making the variational iteration method easier;Applied Mathematics Letters,2019
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