University of Texas at Arlington

Title: Solitons and Nonlinear Partial Differential Equations

Directors: Tuncay Aktosun and Minerva Cordero

Dates of Program: June 1 - July 19, 2008

Summary: Solitary wave solutions (soliton solutions) to four nonlinear partial differential equations (PDEs) are investigated and their applications in various areas are studied. These nonlinear PDEs are the Korteweg-de Vries (KdV) equation u_t-6uu_x+u_xxx=0, the nonlinear SchrÃ¶dinger (NLS) equation iu_t+u_xx+2|u|²u=0, the sine-Gordon equation u_xt=sinu, and the modified Korteweg-de Vries (mKdV) equation u_t+6u²u_x+u_xxx=0. The goal is to obtain soliton solutions to these four equations in a systematic way and to derive the N-soliton solution formula for each equation. Besides working on the theoretical and analytical aspects, the participants will use the symbolic software Mathematica to animate and display such solutions explicitly.