The method of Mn-extension: The KdV equation

Metin Gürses; Aslı Pekcan

doi:10.1016/j.physleta.2024.130217

The method of M_n-extension: The KdV equation

Metin Gürses
, Aslı Pekcan

Division of Applied Mathematics

Bilkent University

Research output: Contribution to journal › Article › peer-review

Abstract

In this work we generalize M₂-extension that has been introduced recently. For illustration we use the KdV equation. We present five different M₃-extensions of the KdV equation and their recursion operators. We give a compact form of M_n-extension of the KdV equation and recursion operator of the coupled KdV system. The method of M_n-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of M₃-extension of KdV.

Original language	English
Article number	130217
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	533
DOIs	https://doi.org/10.1016/j.physleta.2024.130217
Publication status	Published - 15 Feb 2025

Keywords

Coupled systems
Integrability
M-extension
Nonlocal reductions
Recursion operator

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10.1016/j.physleta.2024.130217

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title = "The method of Mn-extension: The KdV equation",

abstract = "In this work we generalize M2-extension that has been introduced recently. For illustration we use the KdV equation. We present five different M3-extensions of the KdV equation and their recursion operators. We give a compact form of Mn-extension of the KdV equation and recursion operator of the coupled KdV system. The method of Mn-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of M3-extension of KdV.",

keywords = "Coupled systems, Integrability, M-extension, Nonlocal reductions, Recursion operator",

author = "Metin G{\"u}rses and Aslı Pekcan",

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T1 - The method of Mn-extension

T2 - The KdV equation

AU - Gürses, Metin

AU - Pekcan, Aslı

PY - 2025/2/15

Y1 - 2025/2/15

N2 - In this work we generalize M2-extension that has been introduced recently. For illustration we use the KdV equation. We present five different M3-extensions of the KdV equation and their recursion operators. We give a compact form of Mn-extension of the KdV equation and recursion operator of the coupled KdV system. The method of Mn-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of M3-extension of KdV.

AB - In this work we generalize M2-extension that has been introduced recently. For illustration we use the KdV equation. We present five different M3-extensions of the KdV equation and their recursion operators. We give a compact form of Mn-extension of the KdV equation and recursion operator of the coupled KdV system. The method of Mn-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of M3-extension of KdV.

KW - Coupled systems

KW - Integrability

KW - M-extension

KW - Nonlocal reductions

KW - Recursion operator

UR - https://www.scopus.com/pages/publications/85214338796

U2 - 10.1016/j.physleta.2024.130217

DO - 10.1016/j.physleta.2024.130217

M3 - Article

AN - SCOPUS:85214338796

SN - 0375-9601

VL - 533

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

M1 - 130217

ER -

The method of M_n-extension: The KdV equation

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Keywords

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