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 Schrödinger (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.

For more information, visit the program webpage at http://omega.uta.edu/~aktosun/nreup2008.

Student Researchers Supported by MAA:

Ernesto Garcia
Carolina Liskey
Carl Looney
Antonio Lopez
Crystal Red Eagle
Sam Rivera

Program Contacts:

Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473

Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470