Non-isospectral variable-coefficient higher-order Korteweg-de Vries equations
| Autor: | W L Chan, Yu-kun Zheng |
|---|---|
| Rok vydání: | 1991 |
| Předmět: |
Variable coefficient
Vries equation Applied Mathematics Mathematics::Analysis of PDEs Computer Science Applications Theoretical Computer Science Nonlinear Sciences::Exactly Solvable and Integrable Systems Isospectral Transformation (function) Signal Processing Order (group theory) Gauge theory Three generations Parametric equation Nonlinear Sciences::Pattern Formation and Solitons Mathematical Physics Mathematical physics Mathematics |
| Zdroj: | Inverse Problems. 7:63-75 |
| ISSN: | 1361-6420 0266-5611 |
| DOI: | 10.1088/0266-5611/7/1/007 |
| Popis: | To the family of nonisospectral variable-coefficient higher-order Korteweg-de Vries equations a new family of nonisospectral variable-coefficient higher-order modified Korteweg-de Vries equations depending on a parametric function eta (t) is constructed. They are connected by an eta 2-dependent Miura transformation. A Backlund transformation is also established. Furthermore, the gauge transformation previously proposed by the authors is applied to this Backlund transformation. For a fixed eta (t), this enables one to derive an autoBacklund transformation for the families of non-isospectral variable-coefficient higher-order eta 2-dependent modified Korteweg-de Vries equations and non-isospectral variable-coefficient higher-order Korteweg-de Vries equations, respectively. As an illustration, three generations of explicit solutions of the non-isospectral second-order variable-coefficient Korteweg-de Vries equation are presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|