Exact solutions of nonlinear evolution equations of the AKNS class
| Autor: | Yu-Kun Zheng, W. L. Chan |
|---|---|
| Rok vydání: | 1989 |
| Předmět: |
Partial differential equation
Differential equation Applied Mathematics Mathematical analysis First-order partial differential equation symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems Method of characteristics Riccati equation symbols Soliton Korteweg–de Vries equation Nonlinear Schrödinger equation Mathematics |
| Zdroj: | The Journal of the Australian Mathematical Society. Series B. Applied Mathematics. 30:313-325 |
| ISSN: | 1839-4078 0334-2700 |
| DOI: | 10.1017/s0334270000006263 |
| Popis: | The problem of obtaining explicit and exact solutions of soliton equations of the AKNS class is considered. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Bäcklund transformations are employed to generate new solutions from the old. Thus, families of new solutions for the KdV equation, the mKdV equation, the sine-Gordon equation and the nonlinear Schrôdinger equation are obtained, avoiding the solution of some Riccati equations. Our results in the KdV case include those obtained recently by other investigators. |
| Databáze: | OpenAIRE |
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