Mathematical Sciences: Forced Solitons and Nonlinear Waves

8901440 吴 该研究计划致力于以下方面 主题： （一）. 孤立子强迫发射的分岔机制 波-通过分析和计算工作来确定， 周期性变化新现象的基本机制 临界激发稳定地应用于 共振时的非线性色散系统。 （二）、 带边界的KdV（Korteweg-de弗里斯）模型 强迫-通过计算机辅助调查， KdV方程初边值问题的理论， 这是一个几乎完全开放的具有挑战性的新领域。本研究 将探讨各种逆变换方法和渐近 近似技术 （三）、 强迫三维非线性波动理论-- 开发有效的数值方法来评估 三维光的产生、散射和衍射 共振时具有外力的非线性波， 分析解的周期分支的判据， 各种案件。 新的研究成果可以应用于所有的孤子轴承 系统，包括流体动力学，海洋工程， 气象学、海洋学、等离子体物理学、光学、多个领域 物理学和量子生物物理学。

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.