Exact Traveling Wave Solutions and Bifurcations of the Time-Fractional Differential Equations with Applications

DOI10.1142/S021812741950041XzbMath1411.35061OpenAlexW2929773227WikidataQ128155844 ScholiaQ128155844MaRDI QIDQ4631674

Yuzhen Bai, Wenjing Zhu, Bei Zhang, Yong-Hui Xia

Publication date: 18 April 2019

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021812741950041x

zbMATH Keywords

exact solutionsolitary wavebifurcationshallow water equationcompactonsmooth periodic waveperiodic peakon

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Explicit solutions, first integrals of ordinary differential equations (34A05) Traveling wave solutions (35C07) Fractional partial differential equations (35R11)

Related Items (19)

Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system ⋮ Exact solutions of a class of nonlinear dispersive long wave systems via Feng's first integral method ⋮ On the Bounds of Lyapunov Exponents for Fractional Differential Systems with an Exponential Kernel ⋮ Bifurcations and Traveling Wave Solutions of Lakshmanan–Porsezian–Daniel Equation with Parabolic Law Nonlinearity ⋮ Traveling wave solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity ⋮ \(PD^\vartheta\) control strategy for a fractional-order chaotic financial model ⋮ Complex behavior analysis of a fractional-order land dynamical model with Holling-II type land reclamation rate on time delay ⋮ An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative ⋮ Explicit exact traveling wave solutions and bifurcations of the generalized combined double \(\sinh\)-\(\cosh\)-Gordon equation ⋮ A unified analysis of exact traveling wave solutions for the fractional-order and integer-order Biswas-Milovic equation: via bifurcation theory of dynamical system ⋮ Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven ⋮ A New Type of Solitary Wave Solution of the mKdV Equation Under Singular Perturbations ⋮ Bifurcations and Exact Solutions for a Class of MKdV Equations with the Conformable Fractional Derivative via Dynamical System Method ⋮ Traveling wave solution of bad and good modified Boussinesq equations with conformable fractional-order derivative ⋮ Traveling wave solutions of a generalized Burgers-\(\alpha\beta\) equation ⋮ Exact traveling wave solutions and bifurcation of a generalized \((3+1)\)-dimensional time-fractional Camassa-Holm-Kadomtsev-Petviashvili equation ⋮ Travelling wave solutions of Wu-Zhang system via dynamic analysis ⋮ The exact solutions of generalized Davey-Stewartson equations with arbitrary power nonlinearities using the dynamical system and the first integral methods ⋮ An algorithm for solving linear nonhomogeneous quaternion-valued differential equations and some open problems

Cites Work

• Unnamed Item
• Unnamed Item
• Dark soliton control in inhomogeneous optical fibers
• On the nonexistence of non-constant exact periodic solutions in a class of the Caputo fractional-order dynamical systems
• Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions
• The first integral method for some time fractional differential equations
• On conformable fractional calculus
• The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
• Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by a new analytical technique
• Exact solutions of the nonlinear Schrödinger equation by the first integral method
• On nonlinear fractional Klein-Gordon equation
• A generalized \((\frac{G'}{G})\)-expansion method for the mKdV equation with variable coefficients
• On the existence of periodic solutions in time-invariant fractional order systems
• On traveling wave solutions to combined KdV-mKdV equation and modified Burgers-KdV equation
• A direct bilinear Bäcklund transformation of a \((2+1)\)-dimensional Korteweg-de Vries-like model
• A proof for non existence of periodic solutions in time invariant fractional order systems
• Solitary wave solutions for a time-fraction generalized hirota-satsuma coupled KdV equation by an analytical technique
• A note on fractional-order derivatives of periodic functions
• Some applications of the \((\frac{G'}{G})\)-expansion method to non-linear partial differential equations
• Family of nonlinear wave equations which yield loop solutions and solitary wave solutions
• A new definition of fractional derivative
• Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
• A multiple exp-function method for nonlinear differential equations and its application
• ON A CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS
• ON NONLINEAR WAVE EQUATIONS WITH BREAKING LOOP-SOLUTIONS
• The first-integral method to study the Burgers–Korteweg–de Vries equation
• Bifurcations of traveling wave solutions for an integrable equation
• Peakon, pseudo-peakon, and cuspon solutions for two generalized Camassa-Holm equations

This page was built for publication: Exact Traveling Wave Solutions and Bifurcations of the Time-Fractional Differential Equations with Applications