Lie symmetry analysis, conservation laws and analytical solutions for a generalized time-fractional modified KdV equation

DOI10.1080/17455030.2018.1450538zbMath1505.35357OpenAlexW2792464015MaRDI QIDQ5104260

Xiu-Bin Wang, Shou-Fu Tian, Chun-Yan Qin, Tian-Tian Zhang

Publication date: 9 September 2022

Published in: Waves in Random and Complex Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17455030.2018.1450538

zbMATH Keywords

conservation lawsLie group analysisgeneralized time fractional modified KdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Fractional partial differential equations (35R11)

Related Items (2)

Approximate symmetries, conservation laws and numerical solutions for a class of perturbed linear wave type system ⋮ LIE SYMMETRY ANALYSIS TO FISHER'S EQUATION WITH TIME FRACTIONAL ORDER

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bäcklund transformation, infinite conservation laws and periodic wave solutions to a generalized \((2+1)\)-dimensional Boussinesq equation
• Group classification of nonlinear time-fractional diffusion equation with a source term
• Initial-boundary value problems for the general coupled nonlinear Schrödinger equation on the interval via the Fokas method
• Rogue waves, homoclinic breather waves and soliton waves for the \((2 + 1)\)-dimensional B-type Kadomtsev-Petviashvili equation
• Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations
• Quasi-periodic waves and solitary waves to a generalized KdV-Caudrey-Dodd-Gibbon equation from fluid dynamics
• Dynamics of the breathers, rogue waves and solitary waves in the \((2+1)\)-dimensional Ito equation
• On Lie symmetries, optimal systems and explicit solutions to the Kudryashov-Sinelshchikov equation
• Nonlinear self-adjointness, conservation laws and exact solutions of time-fractional Kompaneets equations
• Conservation laws for time-fractional subdiffusion and diffusion-wave equations
• A new conservation theorem
• On symmetry-preserving difference scheme to a generalized Benjamin equation and third-order Burgers equation
• The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation
• Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives
• The exact analytic solutions of a nonlinear differential iterative equation
• Riemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques \((G^{\prime} / G)\)-expansion method and improved \((G^{\prime} / G)\)-expansion method
• Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval
• Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation
• Solitary waves, homoclinic breather waves and rogue waves of the (3 + 1)-dimensional Hirota bilinear equation
• On integrability and quasi-periodic wave solutions to a \((3+1)\)-dimensional generalized KdV-like model equation
• Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann-Liouville derivative
• The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics
• On periodic wave solutions with asymptotic behaviors to a \((3+1)\)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid dynamics
• Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations
• Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
• On the Lie algebras, generalized symmetries and Darboux transformations of the fifth-order evolution equations in shallow water
• Invariant analysis and exact solutions of nonlinear time fractional Sharma-Tasso-Olver equation by Lie group analysis
• Lie Symmetry Analysis and Conservation Laws of a Generalized Time Fractional Foam Drainage Equation
• On the integrability of a generalized variable-coefficient Kadomtsev–Petviashvili equation
• Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition
• Lie Symmetry Analysis, Conservation Laws and Exact Power Series Solutions for Time-Fractional Fordy–Gibbons Equation
• Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method
• Invariant variation problems
• Initial-boundary value problems of the coupled modified Korteweg–de Vries equation on the half-line via the Fokas method
• The generalized KaupߝBoussinesq equation: multiple soliton solutions
• Lie symmetry analysis, conservation laws and explicit solutions for the time fractional Rosenau-Haynam equation
• The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method
• On the Integrability of a Generalized Variable‐Coefficient Forced Korteweg‐de Vries Equation in Fluids
• Symmetries and differential equations

This page was built for publication: Lie symmetry analysis, conservation laws and analytical solutions for a generalized time-fractional modified KdV equation