1-soliton solution of the nonlinear Schrödinger's equation with Kerr law nonlinearity using Lie symmetry analysis

DOI10.1007/S10773-009-9957-5zbMath1171.81371OpenAlexW2051603533MaRDI QIDQ842585

Chaudry Masood Khalique, Anjan Biswas

Publication date: 25 September 2009

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-009-9957-5

zbMATH Keywords

solitonsLie symmetryKerr law

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie groups to the sciences; explicit representations (22E70) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (4)

Painlevé analysis and invariant solutions of Vakhnenko-Parkes (VP) equation with power law nonlinearity ⋮ Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations ⋮ Lie symmetry analysis, explicit solutions and conservation laws for the time fractional Kolmogorov–Petrovskii–Piskunov equation ⋮ Stationary solution of the nonlinear Schrödinger's equation with log law nonlinearity by Lie symmetry analysis

Cites Work

• Exact solutions for the quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity
• An exact invariant for a class of time-dependent anharmonic oscillators with cubic anharmonicity
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Symmetries and differential equations
• Unnamed Item
• Unnamed Item

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