Formal variable separation approach for nonintegrable models
- 1 December 1999
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 40 (12), 6491-6500
- https://doi.org/10.1063/1.533103
Abstract
Using a formal variable separation approach, a nonlinear partial differential equation can be solved by solving ordinary different equations or even algebraic equations. Taking the KdV–Burgers and modified KdV–Burgers equations with background interaction as simple examples, some explicit solitary wave solutions which are induced by background source and nonlinearity or dispersion are obtained.Keywords
This publication has 11 references indexed in Scilit:
- Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equationsJournal of Mathematical Physics, 1994
- A new truncation in Painleve analysisJournal of Physics A: General Physics, 1993
- On the interaction of solitons for a class of integrable systems in the spacetime R n+1Letters in Mathematical Physics, 1992
- (1+1)-dimensional integrable systems as symmetry constraints of (2+1)-dimensional systemsPhysics Letters A, 1991
- The constraint of the Kadomtsev-Petviashvili equation and its special solutionsPhysics Letters A, 1991
- Similarity reductions of the KP equation by a direct methodJournal of Physics A: General Physics, 1991
- New similarity reductions of the Boussinesq equationJournal of Mathematical Physics, 1989
- Exact solutions for some nonlinear equationsPhysics Letters A, 1989
- Effect of Weak Dislocation Potential on Nonlinear Wave Propagation in Anharmonic CrystalJournal of the Physics Society Japan, 1974
- Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of SolitonsPhysical Review Letters, 1971