Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation

DOI10.1016/j.amc.2018.03.011zbMath1427.35004arXiv1803.01622OpenAlexW2793102522WikidataQ115361264 ScholiaQ115361264MaRDI QIDQ2333201

T. Kanna, K. Sakkaravarthi, A. Durga Devi, Muthusamy Lakshmanan, Andrew Gratien Johnpillai

Publication date: 12 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.01622

zbMATH Keywords

Painlevé analysissymmetry reductionnonlinear Helmholtz equationLie symmetry analysismodified Prelle-Singer methodperiodic and solitary waves

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items

Computing solitary wave solutions of coupled nonlinear Hirota and Helmholtz equations, On the existence of solution, Lie symmetry analysis and conservation law of magnetohydrodynamic equations, On the integrability aspects of nonparaxial nonlinear Schrödinger equation and the dynamics of solitary waves, Exact solutions of the two-dimensional Cattaneo model using Lie symmetry transformations, Cubic-quintic nonlinear Helmholtz equation: Modulational instability, chirped elliptic and solitary waves

Uses Software

• SYMMGRP

Cites Work

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• Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations
• Lie transformations, nonlinear evolution equations, and Painlevé forms
• Elementary First Integrals of Differential Equations
• Lie symmetries of a generalised nonlinear Schrodinger equation: I. The symmetry group and its subgroups
• Group-Invariant Solutions of Differential Equations
• Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I
• Solving second-order ordinary differential equations by extending the Prelle-Singer method
• On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations
• Symmetries and differential equations