University of Texas at Arlington
Title:
Exact Solutions to Nonlinear Partial Differential Equations
Director(s):
Tuncay Aktosun, Minerva Cordero
Email:
aktosun@uta.edu
Dates of
Program: June 3-July 15, 2007
Summary:
The research topic is exact solutions to two nonlinear partial differential equations (PDEs),
known as the Korteweg-de Vries (KdV) equation
ut-6uux+uxxx=0
and the nonlinear Schrödinger (NLS) equation iut+uxx+2|u|2u=0.
The goal is to obtain exact solutions to these equations
in a systematic way in terms of elementary functions
(exponential, trigonometric, and polynomial functions of x and t).
Exact solutions
will be constructed in terms of triplets A, B, C, where
A is a constant pÃ?p matrix, B is a constant
column p-vector, and C is a constant p-row vector, where
p is any positive integer. Such solutions involve matrix
exponentials.
In the special case
p=1 such solutions include the so-called one-soliton solution.
The special case where A is a diagonal matrix includes all multisoliton
solutions. 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/nreup2007/
Student
Researchers Supported by MAA:
- Danielle Williams
- Jorge Ibanez
- Felipe Mulford
- Antonio Lopez
- Dominique Collins
Program Contacts:
Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473
Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470