Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation

The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is inv...

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Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 11; p. 1632
Main Authors Kudryashov, Nikolay A., Lavrova, Sofia F.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2024
Subjects
Algebra
Analysis
analytical solution
derivative Schrödinger equation
integrability
Nonlinear equations
Nonlinear theories
Optical fibers
Ordinary differential equations
Painlevé test
Partial differential equations
Pulse propagation
Schrodinger equation
simplest equation method
Solitary waves
Traveling waves
Traveling-wave tubes
Wave propagation
Russia
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Summary:The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevé test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrödinger equations and may be used for the description of optical solitons in a nonlinear medium.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12111632