Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2+1)-dimensional AKNS equation

DOI10.3934/CAM.2023024zbMATH Open1544.35018MaRDI QIDQ6579790

Sixing Tao

Publication date: 26 July 2024

Published in: Communications in Analysis and Mechanics (Search for Journal in Brave)

zbMATH Keywords

conservation lawsmultiplier techniqueNoether's theoremAblowitz-Kaup-Newell-Segur (AKNS) equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Other special methods applied to PDEs (35A25) Systems of nonlinear higher-order PDEs (35G50)

Cites Work

• Title not available (Why is that?)
• The periodic wave solutions for a \((2+1)\)-dimensional \textit{AKNS} equation
• \(N\)-soliton solutions for shallow water waves equations in \((1+1)\) and \((2+1)\) dimensions
• The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
• Exact travelling wave solutions for the dissipative \((2+1)\)-dimensional AKNS equation
• A Lie symmetry approach to nonlinear Schrödinger's equation with non-Kerr law nonlinearity
• Double reduction of a nonlinear \((2+1)\) wave equation via conservation laws
• A new conservation theorem
• A unified explicit form of Bäcklund transformations for generalized hierarchies of KdV equations
• Exact traveling wave solutions of certain nonlinear partial differential equations using the \(\left(G^{\prime} / G^2\right)\)-expansion method
• Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies
• Lie symmetry analysis, optimal system, new solitary wave solutions and conservation laws of the Pavlov equation
• Symmetries and exact solutions via conservation laws for some partial differential equations of mathematical physics
• CRE solvability and soliton-cnoidal wave interaction solutions of the dissipative \((2+1)\)-dimensional AKNS equation
• Comment on ‘Conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives’
• Lie symmetry analysis, conservation laws and analytical solutions for chiral nonlinear Schrödinger equation in (2 + 1)-dimensions
• Invariant variation problems
• Darboux transformations of integrable couplings and applications
• Dynamical analysis of diversity lump solutions to the (2+1)-dimensional dissipative Ablowitz–Kaup–Newell–Segure equation
• Multi-soliton solutions for the three types of nonlocal Hirota equations via Riemann–Hilbert approach
• Bidirectional solitons and interaction solutions for a new integrable fifth-order nonlinear equation with temporal and spatial dispersion
• Novel hybrid solitary waves and shrunken-periodic solutions, solitary Moiré pattern and conserved vectors of the (4 + 1)-Fokas equation

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