In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.
Singular 1-soliton solution of the nonlinear variable-coefficient diffusion reaction and mKdV equations
ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences ; 2016 ; La Rochelle, France
AIP Conference Proceedings ; 1798 , 1
27.01.2017
6 pages
Aufsatz (Konferenz)
Elektronische Ressource
Englisch
British Library Online Contents | 2012
|Soliton-like solutions for the nonlinear schrödinger equation with variable quadratic hamiltonians
British Library Online Contents | 2012
|Soliton solution and other solutions to a nonlinear fractional differential equation
American Institute of Physics | 2017
|Switching Characteristics of Variable Coupling Coefficient Nonlinear Directional Coupler
British Library Online Contents | 2004
|