Exact solutions of a KdV equation hierarchy with variable coefficients. (English) Zbl 1326.35326
Summary: In this paper, a nonisospectral and variable-coefficient KdV equation hierarchy with self-consistent sources is derived from the related linear spectral problem. Exact solutions of the KdV equation hierarchy are obtained through the inverse scattering transformation (IST). It is shown that the IST is an effective mathematical tool for solving the whole hierarchy of nonisospectral nonlinear partial differential equations with self-consistent sources.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C05 | Solutions to PDEs in closed form |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35P25 | Scattering theory for PDEs |
| 35R30 | Inverse problems for PDEs |
Keywords:
nonlinear partial differential equation; exact solution; KdV equation hierarchy; spectral problem; inverse scattering transformationReferences:
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