The generalized Wronskian solutions of the integrable variable-coefficient Korteweg-de Vries equation. (English) Zbl 1247.35137
Summary: A broad set of sufficient conditions consisting of systems of linear partial differential equations are presented which guarantee that the Wronskian determinant is the solutions of the integrable variable-coefficient Korteweg-de Vries model from Bose-Einstein condensates and fluid dynamics. The generalized Wronskian solutions provide us with a comprehensive approach to construct many exact solutions including rational solutions, solitons, negatons, positons, and complexitons.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C08 | Soliton solutions |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
Wronskian determinant; solitons; rational solutions; positons; negatons; complexitons; variable-coefficient KdV equationReferences:
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