Soliton with non-constant velocity. (English) Zbl 1013.35075
Summary: This article develops the dressing method for the investigation of non-integrable in classical sense nonlinear partial differential equations (PDEs). We construct a \((1+1)\)-dimensional family of nonlinear PDEs which admits a specific type of soliton-like solutions whose velocity depends on the space coordinate. Analogy of zero-curvature representation is discussed briefly.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
References:
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