Bifurcation and new exact traveling wave solutions for time-space fractional Phi-4 equation
Zhao Li, Tianyong Han, Chun Huang
Abstract
In this paper, the dynamical behavior of a time-space fractional Phi-4 equation is investigated by utilizing the bifurcation method of a planar dynamical system. Under the given parameter conditions, phase portraits and bifurcations are obtained with the help of the mathematical software Maple. Moreover, some new exact traveling wave solutions are obtained, such as Jacobi elliptic function solutions, hyperbolic function solutions, trigonometric function solutions, kink solitary wave solutions, and periodic wave solutions.
Topics & Concepts
Phase portraitBifurcationMathematical analysisTrigonometric functionsMapleHyperbolic functionFunction (biology)Traveling waveSinusoidal plane-wave solutions of the electromagnetic wave equationElliptic functionPhase spaceMathematicsDynamical systems theoryPhysicsNonlinear systemGeometryQuantum mechanicsBotanyOptical fieldElectromagnetic wave equationEvolutionary biologyBiologyMagnetic fieldNonlinear Waves and SolitonsFractional Differential Equations SolutionsAdvanced Differential Equations and Dynamical Systems