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Dynamical analysis has revealed that, for some nonlinear wave equations, loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loopsoliton solution consists of three solutions, and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a “real” loop-solution exists, and if so, what are the precise parametric representations of these loop traveling wave solutions. [ABSTRACT FROM AUTHOR]

By using the dynamical system method to study the 2D-generalized Benney-Luke equation, the existence of kink wave solutions and uncountably infinite many smooth periodic wave solutions is shown. Explicit exact parametric representations for solutions of kink wave, periodic wave and unbounded traveling wave are obtained. [ABSTRACT FROM AUTHOR]

By using the method of dynamical systems, the travelling wave solutions of for an integrable nonlinear evolution equation is studied. Exact explicit parametric representations of kink and anti-kink wave, periodic wave solutions and uncountably infinite many smooth solitary wave solutions are given. [ABSTRACT FROM AUTHOR]

By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations, the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travelling wave solutions is studied and the bifurcation parametric sets are shown. Under the given parametric conditions, all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained. [ABSTRACT FROM AUTHOR]

By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined. [ABSTRACT FROM AUTHOR]

For a given system, by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle, the exact computation formula of the third separatrix values named by Leontovich for the multiple limit cycle bifurcation was given, which was one of the main criterions for the number of limit cycles bifurcated from a homoclinic orbit and the stability of the homoclinic loop, and a computation formula for higher separatrix values was conjectured. [ABSTRACT FROM AUTHOR]

The attraction domain of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated again by using of some analysis techniques and Liapunov method, some new results are obtained, that can be used for evaluation of fault-tolerance capability and the synthesis procedures for continuous feedback associative memory neural networks. [ABSTRACT FROM AUTHOR]

By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three-dimensional square cell pattern of Rayleigh-Benard convection. The result means that our method enables this three-dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained. [ABSTRACT FROM AUTHOR]