The logarithmic \((1+1)\)-dimensional KdV-like and \((2+1)\)-dimensional KP-like equations: Lie group analysis, conservation laws and double reductions

DOI10.1515/ijnsns-2017-0275OpenAlexW2969432516WikidataQ115236227 ScholiaQ115236227MaRDI QIDQ2296133

Emrullah Yaşar, İlker Burak Giresunlu, Abdullahi Rashid Adem

Publication date: 17 February 2020

Published in: International Journal of Nonlinear Sciences and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ijnsns-2017-0275

zbMATH Keywords

conservation lawsmultiplierLie symmetry groupnonlinear self-adjointnesssimplest equation methodgeneralized double reduction

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (1)

Conservation laws, soliton solutions and modulation instability for the coupled Gerdjikov-Ivanov equations

Uses Software

• GeM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symmetries and solutions of a third order equation
• Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearities
• A KdV-like advection-dispersion equation with some remarkable properties
• Generalization of the double reduction theory
• GeM software package for computation of symmetries and conservation laws of differential equations
• A new conservation theorem
• Applications of symmetry methods to partial differential equations
• Relationship between symmetries and conservation laws
• Conservation laws and exact solutions of a class of non linear regularized long wave equations via double reduction theory and Lie symmetries
• Homotopy perturbation technique
• Simplest equation method to look for exact solutions of nonlinear differential equations
• A multiple exp-function method for nonlinear differential equations and its application
• Nonlinear self-adjointness and conservation laws
• The tanh method: I. Exact solutions of nonlinear evolution and wave equations

This page was built for publication: The logarithmic \((1+1)\)-dimensional KdV-like and \((2+1)\)-dimensional KP-like equations: Lie group analysis, conservation laws and double reductions