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 ut-6uux+uxxx=0, the nonlinear Schrödinger (NLS) equation iut+uxx+2|u|2u=0, the sine-Gordon equation uxt=sinu, and the modified Korteweg-de Vries (mKdV) equation ut+6u2ux+uxxx=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
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