| 提要文摘： | the studies of solitons and complete integrability of nolinear wave equations and bifurcations and chaos of dynamical systems are two very active fields in nonlinear sceince.because a homocinic orbit of a travelling wave system(odes)corresponds to a solitary wave solution of a nonlinear wave equation(pde).this fact provides an intersection point for the above two study fields.the aim of this book is to give a more systematic account for the bifurcation theory method of dynamical systems to find exact travelling wave solutions and their dynamics with an emphasis on the singular properties(so called"new waves mathematics")of solutions,such as peakons,cuspons,compactons and loop solutions et al.,for some classes of very well known nonlinear wave equations.readers shall find how standard methods of the theory of dynamical systems may be used of the study of travelling wave solutions even in the case of systems with discontinuities. |
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