Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	虞国富教授，上海交通大学
Inviter:	胡星标研究员
Title:	Integrable discretization and numerical simulations of the generalized coupled integrable dispersionless equations
Time & Venue:	2018.12.27 20:00-21:00 N702
Abstract:	In this talk, we study the generalized coupled integrable dispersionless (GCID) equations and construct two integrable discrete analogues including a semi-discrete system and a full-discrete one. The results are based on the relations among the GCID equations, the sine-Gordon equation and the two-dimensional Toda lattice equation. We also present the $N$-soliton solutions to the semi-discrete and fully discrete system in the form of Casorati determinant. In the continuous limit, we show that the fully discrete GCID equations converge to the semi-discrete GCID equations, then further to the continuous GCID equations. By using the integrable semi-discrete system, we design two numerical schemes to the GCID equations and carry out several numerical experiments with solitons and breather solutions. This is a joint work with Ying-Nan Zhang.