Abstract
Four (2+1)-dimensional nonlinear evolution equations, generated by the Jaulent-Miodek hierarchy, are investigated by the bifurcation method of planar dynamical systems. The bifurcation regions in different subsets of the parameters space are obtained. According to the different phase portraits in different regions, we obtain kink (antikink) wave solutions, solitary wave solutions, and periodic wave solutions for the third of these models by dynamical system method. Furthermore, the explicit exact expressions of these bounded traveling waves are obtained. All these wave solutions obtained are characterized by distinct physical structures.
Highlights
In [1,2,3,4], four (2+1)-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy were developed
In [11], only considering bifurcation parametric c, some exact traveling wave solutions are given by applying the method of dynamical systems for these models
By determining the necessary condition for the complete integrability of these models in [3], multiple kink solutions and multiple singular kink solutions were formally derived for the third model
Summary
In [1,2,3,4], four (2+1)-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy were developed. Noting (6), we obtain the following exact solitary wave solutions (see Figure 5(a)) of the system (11) from (33): q2 (x, y, t). Completing the above integral, we obtain the following solitary wave solution (see Figure 6(a)) of the system (11):. Completing the above integral (46a), we obtain the following kink wave solution of the system (11) (see Figure 7(a)):. Completing the above integral (55a), we obtain the exact kink wave solution of the system (11) (see Figure 8(a)): φ5 (ξ) =. Not considering the necessary condition for the kink waves to exist [3], we obtain all kink and antikink wave solutions of the system (11) and the system (3) by the bifurcation method of dynamical systems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
