Summary:   Determination of solitary waves plays an important role in the study of nonlinear wave equations in physical systems. Efficient and accurate numerical methods for solitary waves in two or three spatial dimensions have remained a challenge. In this talk, we analyze an efficient numerical iteration method --- the imaginary-time evolution method, for determining solitary waves in arbitrary spatial dimensions. First, convergence conditions of this method are explicitly obtained. Second, it is proved that for nodeless solitary waves, this method converges if and only if the solitary wave is linearly stable. This connection between convergence and linear stability is a novel property of this numerical scheme which has not been seen before. Thirdly, we propose an accelerated imaginary-time evolution method which has the same convergence conditions as the original method but with a drastically improved convergence rate. Conditions for optimal acceleration are also explicitly derived. Lastly, the performance of the proposed methods is illustrated by applying them to examples of physical interest, such as the two-dimensional nonlinear Schroedinger equations with localized and periodic potentials and the Kadomtsev-Petviashvili equation. This work was done in collaboration with T. Lakoba at University of Vermont.

杨建科教授：1989年毕业于清华大学应用数学系， 1994年获麻省理工学院应用数学博士学位，同年去University of Vermont数学系任教至今。杨教授最近十年的工作主要集中在非线性光学的理论研究方面。迄今为止，他共发表SCI论文57篇, 经过评审的学术会议专辑论文8篇，论文被SCI杂志引用470多次，获得的科研经费一百多万美元，指导过博士后两名，担任国际学术杂志编委一个，国际学术会议委员会成员一次，及国际会议特邀报告两次。

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