The bifurcation and chaotic motion of some nonlinear relative rotation system with heteroclinic orbit is studied. By using dissipative system Lagrange equation, the dynamics equation of nonlinear relative rotation system under combination harmonic excitations is established. Firstly, the bifurcation response equation of relative rotation system under combination resonance is deduced with the method of multiple scales. Singularity analysis is employed to obtain the transition set of steady motion. Secondly, the Melnikov function of heteroclinic orbit is solved according to heteroclinic orbit parameter equation of relative rotation system. The critical condition of chaos about Smale commutation is given. Finally, numerical method is employed to analyze the influences of different system parameters on chaotic motion by bifurcation diagram, the maximum Lyapunov, phase trajectory and Poincare map.
We present a family of the solutions of two-component Bose-Einstein condensates with time-dependent scattering length by means of multiple-scale method. Our numerical calculations show that the collision properties (the position, the time, and the frequency of the collision) between two solitons can be controlled by the time-dependent interspecies scattering length. Meanwhile, we also find that the amplitude of the solitons is close related to the timedependent interspecies scattering length.
By using multiple-scale method, we analytically study the soliton dynamics of Bose–Einstein condensate (BEC) trapped in a double square well potential. It is shown that dark soliton can be stable, which is generated in BEC trapped in a double square well. The amplitude and the width of dark soliton are related to the initial position of the soliton. Within the double square well, because of the confinement of the potential, the amplitude of the dark soliton is larger, while the width of the dark soliton is smaller. Furthermore, we also find that the amplitude and the width of the soliton are closely related to the depth of the double square well. With the increase of the depth, the amplitude of the dark soliton increases remarkably, while the width of the dark soliton decreases slowly.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.