Compacton and solitary pattern solutions for nonlinear dispersive KdV-type equations involving Jumarie's fractional derivative

DOI10.1016/j.physleta.2011.11.013zbMath1255.35218OpenAlexW2057298644MaRDI QIDQ1933055

Ye Fang, Shimin Guo, Liquan Mei, Zhi-Yu Qiu

Publication date: 22 January 2013

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2011.11.013

zbMATH Keywords

fractional differential equationmodified Riemann-Liouville derivativeKdV-type equationssolitary pattern solutioncompacton solution

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Iteration theory, iterative and composite equations (39B12) Soliton solutions (35C08) Fractional partial differential equations (35R11) Pattern formations in context of PDEs (35B36)

Related Items (6)

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations ⋮ An efficient Galerkin spectral method for two-dimensional fractional nonlinear reaction-diffusion-wave equation ⋮ Fractional variational homotopy perturbation iteration method and its application to a fractional diffusion equation ⋮ Exact solutions of fractional heat-like and wave-like equations with variable coefficients ⋮ Improved \((G'/G)\)-expansion method for the space and time fractional foam drainage and KdV equations ⋮ Solitary solutions for time-fractional nonlinear dispersive PDEs in the sense of conformable fractional derivative

Cites Work

• Unnamed Item
• Fractional variational iteration method and its application
• The fractional variational iteration method using He's polynomials
• Fractional sub-equation method and its applications to nonlinear fractional PDEs
• Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order
• Auxiliary equation method for the mKdV equation with variable coefficients
• Compact and noncompact solutions for nonlinear dispersive variants of the generalized KdV equation
• Beyond Adomian polynomials: He polynomials
• Solitary solutions for the nonlinear dispersive \(K(m,n)\) equations with fractional time derivatives
• Compact finite difference method for the fractional diffusion equation
• The extended \(\left( \frac {G^{\prime}}{G}\right)\)-expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations
• Variational iteration method: New development and applications
• Exact special solutions to the nonlinear dispersive \(K(2,2,1)\) and \(K(3,3,1)\) equations by He's variational iteration method
• A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
• An exact solution of start-up flow for the fractional generalized Burgers' fluid in a porous half-space
• Compact and noncompact dispersive patterns
• Variational iteration method for fractional heat- and wave-like equations
• On the general Taylor theorem and its applications in solving nonlinear problems
• Fractional master equation: Non-standard analysis and Liouville-Riemann derivative
• A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
• On solitons, compactons, and Lagrange maps.
• Homotopy perturbation technique
• New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems
• Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution
• Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results
• Analytical solution of the linear fractional differential equation by Adomian decomposition method
• Explicit travelling wave solutions of variants of the \(K(n,n)\) and the \(ZK(n,n)\) equations with compact and noncompact structures
• Soliton solutions for the fifth-order KdV equation and the Kawahara equation with time-dependent coefficients
• Evolution equations for stratified dilute suspensions
• Compactons: Solitons with finite wavelength
• Exact special solutions with solitary patterns for the nonlinear dispersive \(K(m,n)\) equations

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