Painlevé analysis of the resonant third-order nonlinear Schrödinger equation. (English) Zbl 07901114
Summary: The resonant Schrödinger equation of the third order is studied. The Painlevé test for nonlinear partial differential equations is used to determine integrability of equation. It is shown that the necessary condition for integrability of partial differential equations by the inverse scattering transform is fulfilled at certain parameter restriction. Analytical solutions in the form of periodic and solitary wave are presented.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35C08 | Soliton solutions |
| 35B10 | Periodic solutions to PDEs |
| 35A20 | Analyticity in context of PDEs |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
resonant third-order nonlinear Schrödinger equation; Painlevé test; integrability; solitary and periodic waveSoftware:
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