Bifurcation and new exact traveling wave solutions for time-space fractional Phi-4 equation
Source abstract
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.
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Research context
OpenAlex topics: Nonlinear Waves and Solitons · Fractional Differential Equations Solutions · Advanced Differential Equations and Dynamical Systems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
College of Computer Science, Chengdu University 1 , Chengdu 610106, People’s Republic of China
Faculty of Education, Sichuan Vocational and Technical College 2 , Suining 629000, People’s Republic of China
Funding
The Education Department of Sichuan Province of China · Scientific Research Funds of Chengdu University
References (39)
Show source-provided references
1. Bifurcations and solutions for the generalized nonlinear Schrödinger equation10.1016/j.physleta.2019.126028 ↗
2. The generalized bifurcation method for deriving exact solutions of nonlinear space-time fractional partial differential equations10.1016/j.amc.2019.124735 ↗
3. On explicit exact solutions and conservation laws for time fractional variable-coefficient coupled Burger’s equations10.1016/j.cnsns.2019.105108 ↗
4. Exact solutions of space-time fractional EW and modified EW equations10.1016/j.chaos.2017.01.015 ↗
5. Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations10.1016/j.amc.2016.03.032 ↗
6. An implicit midpoint difference scheme for the fractional Ginzburg–Landau equation10.1016/j.jcp.2016.02.018 ↗
7. An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg–Landau equations10.1016/j.camwa.2017.12.005 ↗
8. Galerkin finite element method for the nonlinear fractional Ginzburg–Landau equation10.1016/j.apnum.2017.03.003 ↗
9. Fast iterative solvers and simulation for the space fractional Ginzburg–Landau equations10.1016/j.camwa.2019.01.026 ↗
10. Periodic soliton interactions for higher-order nonlinear Schrödinger equation in optical fibers10.1007/s11071-020-05649-9 ↗
11. Darboux transformation and analytic solutions for a generalized super-NLS-mKdV equation10.1007/s11071-019-05275-0 ↗
12. Periodic transmission and control of optical solitons in optical fibers10.1016/j.ijleo.2020.164752 ↗
13. Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives10.1016/j.ijleo.2016.08.076 ↗
14. The first integral method for the time fractional Kaup–Boussinesq system with time dependent coefficient10.1016/j.amc.2014.12.094 ↗
15. Exact solution of certain time fractional nonlinear partial differential equations10.1007/s11071-016-2714-4 ↗
16. Ideal of invariant subspace combined with elementary integral method for investigating exact solutions of time-fractional NPDEs10.1016/j.amc.2018.07.033 ↗
17. A new improved Adomian decomposition method and its application to fractional differential equations10.1016/j.apm.2012.03.016 ↗
18. Analytical solution for the space fractional diffusion equation by two-step Adomian decomposition method10.1016/j.cnsns.2008.01.010 ↗
19. Lie symmetry analysis and exact solutions of the time-fractional biological population model10.1016/j.physa.2019.123134 ↗
20. Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey–Dodd–Gibbon–Sawada–Kotera equation10.1016/j.cnsns.2017.11.015 ↗
21. The homotopy analysis method for solving the time-fractional Fornberg–Whitham equation and comparison with Adomian’s decomposition method10.1016/j.apm.2013.03.074 ↗
22. (G′/G)-expansion method for solving fractional partial differential equations in the theory of mathematical physics10.1088/0253-6102/58/5/02 ↗
23. Applications of homogenous balanced principle on investigating exact solutions to a series of time fractional nonlinear PDEs10.1016/j.cnsns.2016.11.018 ↗
24. Method of separation variables combined with homogenous balanced principle for searching exact solutions of nonlienar time-fractional biological population model10.1016/j.cnsns.2018.03.009 ↗
25. Applications of integral bifurcation method together with homogeneous balanced principle on investigating exact solutions of time fractional nonlinear PDEs10.1007/s11071-017-3904-4 ↗
26. Exact traveling wave solutions of the space-time fractional complex Ginzburg–Landau equation and the space-time fractional Phi-4 equation using reliable methods10.1186/s13662-019-2154-9 ↗
27. Analytical solution of the time-fractional Phi-4 equation by using modified residual power series method10.1007/s11071-017-3820-7 ↗
28. New approach for exact solutions of time fractional Cahn–Allen equation and time fractional Phi-4 equation10.1016/j.physa.2016.12.081 ↗
29. Two reliable techniques for the analytical study of conformable time-fractional Phi-4 equation10.1007/s11082-017-1288-9 ↗
30. Conservation laws and exact solutions of Phi-four (Phi-4) equation via the (G′/G, 1/G)-expansion method10.1515/zna-2016-0010 ↗
31. Exact solutions to the Benney–Luke equation and the Phi-4 equations by using modified simple equation method10.1016/j.rinp.2015.01.008 ↗
32. New exact solutions of nonlinear conformable time-fractional Phi-4 equation10.1016/j.cjph.2018.08.001 ↗
33. Exact periodic and explicit solutions of the conformable time fractional Ginzburg Landau equation10.1007/s11082-018-1420-5 ↗
34. 2007
35. Smooth and non-smooth traveling waves in a nonlinearly dispersive equation10.1016/s0307-904x(00)00031-7 ↗
36. 1999
37. Bifurcations and exact solutions of AC-driven complex Ginzburg–Landau equation10.1016/j.amc.2013.05.067 ↗
38. Bifurcations and exact travelling wave solutions for Gardner-KP equation10.1016/j.amc.2013.12.005 ↗
39. Qualitative analysis and traveling wave solutions for the perturbed nonlienear Schrödinger equation with Kerr law nonlienearity10.1016/j.physleta.2010.11.070 ↗