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

Nikolay A. Kudryashov () and Sofia F. Lavrova
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Nikolay A. Kudryashov: Moscow Engineering Physics Institute ( MEPI), National Research Nuclear University, 31 Kashirskoe Shosse, 115409 Moscow, Russia
Sofia F. Lavrova: Moscow Engineering Physics Institute ( MEPI), National Research Nuclear University, 31 Kashirskoe Shosse, 115409 Moscow, Russia

Mathematics, 2024, vol. 12, issue 11, 1-13

Abstract: 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.

Keywords: derivative Schrödinger equation; Painlevé test; integrability; analytical solution; simplest equation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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