Zhang Jin E, Li Yishen
Department of FINA, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jan;67(1 Pt 2):016306. doi: 10.1103/PhysRevE.67.016306. Epub 2003 Jan 24.
A theory of bidirectional solitons on water is developed by using an integrable Boussinesq surface-variable equation. We present an explicit transformation between the system and a member of the Ablowitz-Kaup-Newell-Segur system, and derive an exact multisoliton solution by using a Darboux transformation. The phase shifts and the maximum wave heights during the interaction are studied for two-soliton overtaking and head-on collisions. They agree with the Korteweg-de Vries solution for overtaking collision and the perturbation solution for head-on collision.
利用一个可积的布辛涅斯克表面变量方程，建立了水面上双向孤子的理论。我们给出了该系统与阿布洛维茨 - 考普 - 纽厄尔 - 西格系统中的一个成员之间的显式变换，并通过达布变换导出了精确的多孤子解。研究了两孤子超车和迎头碰撞时相互作用过程中的相移和最大波高。它们与超车碰撞的科特韦格 - 德弗里斯解以及迎头碰撞的微扰解一致。
