Mathematical Sciences: Forced Solitons and Nonlinear Waves

点击翻译按钮获取中文摘要

8901440 Wu This research program is devoted to the following subjects: (1). Bifurcation mechanism of forced emision of solitary waves - to determine by analytical and computational efforts, the basic mechanism underlying the new phenomena of periodic emision of solitons by critical excitations steadily applied to a nonlinear dispersive system at resonance. (2). The KdV (Korteweg-de Vries) model with boundary forcing - to develop, by computer-aided investigations, the theory of initial-boundary-value problems of the KdV equation, a new challenging field which is nearly all open. This study will explore various inverse transform methods and asymptotic approximation techniques. (3). Forced three-dimensional nonlinear wave theory - to develop efficient numerical methods for evaluating the generation, scattering and diffraction of three-dimensional nonlinear waves with external forcing at resonance and to analyze the criteria of periodic bifurcation of solutions in various cases. New research results can be applied to all soliton-bearing systems, including fluid dynamics, ocean engineering, meterology, oceanography, plasma physics, optics, several areas of physics and quantum biophysics.