University of Texas at Arlington
Title:
Solitons and Nonlinear Partial Differential Equations
Directors:
Tuncay Aktosun and Minerva Cordero
Email:
aktosun@uta.edu
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
Support for NREUP is provided by the National Science Foundation Division of Mathematical Sciences, the National Security Agency and The Moody's Foundation.