Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2007-03-19
AnnalsPhys.323:1150-1167,2008
Nonlinear Sciences
Exactly Solvable and Integrable Systems
RevTex, 15 pages, 3 figures; version with new section and references, to appear in Annals of Physics
Scientific paper
10.1016/j.aop.2007.10.003
We propose a simple and direct method for generating travelling wave solutions for nonlinear integrable equations. We illustrate how nontrivial solutions for the KdV, the mKdV and the Boussinesq equations can be obtained from simple solutions of linear equations. We describe how using this method, a soliton solution of the KdV equation can yield soliton solutions for the mKdV as well as the Boussinesq equations. Similarly, starting with cnoidal solutions of the KdV equation, we can obtain the corresponding solutions for the mKdV as well as the Boussinesq equations. Simple solutions of linear equations can also lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve some new families of KdV equations and show how soliton solutions are also obtained for the higher order equations of the KdV hierarchy using this method.
Bazeia Dionisio
Das Ashok
Losano Laercio
Silva Analia
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