For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the general polytropic equation of states is P∝n γ＋1. According to the effective power γ≈0.5~1.3, we resolve the time-dependent nonlinear Schrodinger equation and find series bright solitons. The analysis could help in the search for matter-wave soliton trains in degenerate Femi gas.
This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale atmosphere, which improves the result of [11].
We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2 by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtained here are not required sufficiently large.
CHENG Chong-Qing 1, & LI Xia 2 1 Department of Mathematics, Nanjing University, Nanjing 210093, China
The Myrzakulov-I equation is a 2＋1-dimensional generalization of the Heisenberg ferromagnetic equation and has a non-isospectral Lax pair. The Darboux transformation with non-constant spectral parameter is constructed and an extra constraint on the spectral parameter for the existence of the Darboux transformation is derived. Explicit expressions of the solutions of the Myrzakulov-I equation are presented.
Nonlinear dynamics of the time-delayed Mackey-Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincare section. Synchronizations of the drive-response Mackey-Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.
