报告人: Prof.Thiab Taha （University of Georgia,USA）
Recently, there has been a lot of theoretical and numerical research in order to study the role of nonlinear terms in Korteweg-de Vries-like equations K(m, n):
Ut + ( um)x + (un)xxx = 0, m > 1, n > 0,
Numerical simulations of solutions of K (m, 1) confirm that its solitary wave solutions are unstable if m > 4, and in fact, that neighboring solutions emanating from smooth initial data appear to form singularities in finite time. On the other hand, numerical simulations of solutions of K (m, n), for certain values of m and n, have shown that their solitary wave solutions have compact support.
In this paper an accurate numerical scheme based on a combination of finite difference and inverse scattering transform scheme is used to investigate the above results. A parallel algorithm for the implementation of this scheme on parallel computers is presented. This algorithm is implemented on an intel higher performance computer and the numerical results are discussed.