An Extended KdV Hierarchy via an Energy Dependent Scattering

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J. Math. Sci. Univ. Tokyo
Vol. 29 (2022), No. 3, Page 285-358.

Kamimura, Yutaka
An Extended KdV Hierarchy via an Energy Dependent Scattering
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
This paper formulates an extended KdV hierarchy involving a coupled KdV equation, the Boussinesq system as well as their higher order versions.Based upon an inverse scattering method on an energy dependent Schrödinger operator, $N$-soliton solutions in the extended hierarchy are constructed in a unified fashion.In even-order systems, each soliton is multi-peaked when a parameter exceeds the critical value. The classical solitons in the KdV hierarchy are embedded into those with the parameter being zero of even-order systems.

Keywords: The KdV hierarchy, Energy dependent Schrödinger operator, Inverse scattering method, Reflectionless scattering, Nonlinear evolution system, Soliton solution, Boussinesq system.

Mathematics Subject Classification (2020): 35Q53, 37K10, 37K40, 81U40.

Mathematical Reviews Number: MR4515053

Received: 2022-05-11

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