The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation-Reference-Cited by-同舟云学术

The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation

Published:2023-07-19 Issue:7 Volume:12 Page:703
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Redkina Tatyana V.¹^ORCID,Zakinyan Arthur R.¹²^ORCID,Zakinyan Robert G.¹²^ORCID

Affiliation:

1. North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, Russia

2. Physical-Technical Faculty, North-Caucasus Federal University, 355017 Stavropol, Russia

Abstract

In this paper we consider examples of complex expansion (cKdV) and perturbation (pKdV) of the Korteweg–de Vries equation (KdV) and show that these equations have a representation in the form of the zero-curvature equation. In this case, we use the Lie algebra of 4-dimensional quadratic nilpotent matrices. Moreover, it is shown that the simplest possible matrix representation of this algebra leads to the possibility of constructing a countable number of conservation laws for these equations.

Funder

North-Caucasus Center for Mathematical Research

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/7/703/pdf

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