题 目：Singular nonlinear wave motions in mechanics and physics: dynamical system approach
报告人：李继彬 教授 浙江师范大学
The investigation of the traveling wave solutions to nonlinear evolution equations (NLEEs) plays an important role in the mathematical physics. For example, the wave phenomena observed in fluid dynamics, plasma and elastic media are often medelled by the bell shaped or kink shaped traveling wave solutions. Since 1970's, much significant progress has been made in the development of theory and approach, such as inverse scattering transformation method, Darboux transformation method, Hirota bilinear method, algebraic-geometric method, tanh method and so on.
In [Rosenau and Hyman, 1994] and [Rosenau, 1997], the authors discussed “new wave mathematics” for some new integrable systems with dispersions (for example, K (m, n) equation). So called "new wave", it is named by "peak on", "cusp on" and "compact on" et al., which are different from the bell shaped solitary wave solution. In his "concluding comments" of [Rosenau, 1997] (pp318), for the understanding to the above mentioned nonanalytic wave (i.e. "new wave"), the author stated that "unfortunately, as we have pointed elsewhere in 1994's paper, a lack of proper mathematical tools makes this goal at the present time pretty much beyond our reach."
In order to solve the "mathematical tools" problem, we developed dynamical system method, which provided nice understanding for these "new waves" to two classes of the singular nonlinear traveling wave systems.
This talk introduces our basic mathematical theory to these traveling wave systems and some applications.
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