Department of Mathematics
University of Texas, Pan American
Discrete integrable systems : from nonlinear waves to self-adaptive moving mesh schemes
After the monumental works of Mark Ablowitz and Ryogo Hirota in 1970s, the study of discrete integrable systems has received much attention in various fields such as mathematical physics, numerical algorithms, statistical physics, discrete differential geometry, special functions, combinatorics and cellular automata. Recent intensive studies revealed that mathematical structures of discrete integrable systems are richer than those of continuous integrable systems. Recently, we have investigated integrable discretizations of nonlinear wave equations in which singularities of solutions exist. For PDEs in this class, we obtained discrete integrable systems of self-adaptive moving mesh type which can be used for numerical simulations of nonlinear PDEs. An approach based on discrete differential geometry is effective to construct self-adaptive moving mesh discrete integrable systems. In this talk, I will review recent studies of discrete integrable systems and self-adaptive moving mesh schemes.
Sponsored by the Department of Mathematical Sciences
Host: John Zweck