Lax Pairs for the Modified KdV Equation-Reference-Cited by-同舟云学术

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Lax Pairs for the Modified KdV Equation

Published:2024-02-14 Issue:2 Volume:13 Page:121
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Burde Georgy I.¹^ORCID

Affiliation:

1. Swiss Institute for Dryland Environmental and Energy Research, Jacob Blaustein Institutes for Desert Research, Sede-Boker Campus, Ben-Gurion University, Midreshet Ben-Gurion 84990, Israel

Abstract

Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations, converting the defined Lax pairs to some simpler forms, are found. The direct method and its possible applications to other types of evolution equations are discussed.

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/2/121/pdf

Reference48 articles.

1. Drazin, P.G., and Johnson, R.S. (1990). Solitons: An Introduction, Cambridge University Press.

2. Ablowitz, M.J., and Clarkson, P.A. (1991). Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press.

3. Ablowitz, M., and Segur, H. (1981). Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Mathematics, 4), Society for Industrial and Applied Mathematics (SIAM).

4. Newell, A.C. (1985). Solitons in Mathematics and Physics, Society for Industrial and Applied Mathematics (SIAM).

5. Zakharov, V.E. (1991). What Is Integrability?, Springer.

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