The Derivation of a Fifth-Order Equation via the Lax and the Alternate Lax Methods

Mehmet Ünlü

doi:10.17776/csj.1733907

The Derivation of a Fifth-Order Equation via the Lax and the Alternate Lax Methods

Abstract

We present the derivation of a fifth-order integrable nonlinear partial differential equation via the Lax method and the alternate Lax method in the continuous case. The Lax method uses a pair of differential operators, L and A, satisfying a compatibility condition. The pair (L,A) is known as the Lax pair. The alternate Lax method is a variation of the Lax method and use a consistency relation equivalent to the commutation of a certain derivative operator associated with the time evolution and the spacial evolution. In the paper we also show that the Lax method and the alternate Lax method are equivalent.

Keywords

References

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems , Partial Differential Equations

Journal Section

Research Article

Authors

Mehmet Ünlü ^*
0000-0001-6793-253X
Türkiye

Publication Date

September 30, 2025

Submission Date

July 3, 2025

Acceptance Date

September 3, 2025

Published in Issue

Year 2025 Volume: 46 Number: 3

DOI

https://doi.org/10.17776/csj.1733907

IZ

https://izlik.org/JA66BE68GM

Cite

RIS / Bibtex

APA

Ünlü, M. (2025). The Derivation of a Fifth-Order Equation via the Lax and the Alternate Lax Methods. Cumhuriyet Science Journal, 46(3), 583-589. https://doi.org/10.17776/csj.1733907