University of Texas at Arlington
Title:
Exact Solutions to Nonlinear Evolution Equations
Directors:
- Tuncay Aktosun
- Minerva Cordero
Email:
Dates of Program: June 1 - July 31, 2010
Summary:
Certain nonlinear partial differential equations
and difference equations
are known as integrable evolution equations. They describe time evolution
of various important physical systems, and they
possess certain solutions that can be expressed explicitly
in terms of elementary functions.
Among such equations 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,
the modified Korteweg-de Vries (mKdV) equation
ut+6u2ux+uxxx=0, and
the Toda lattice equation ’2un/’t2
=e-un+un-1-e-un+1+un.
The goal of this research experience
is to analyze various integrable evolution equations in a systematic way,
derive explicit solution formulas for them, understand properties of such solutions,
and visualize the time evolution of those solutions by developing Mathematica animations.
Student
Researchers Supported by MAA:
- April Diaz
- Eleisha Jackson
- Erica Llaca
- Sarah Moorman
- Andrew Velasquez
More Information:
http://omega.uta.edu/~aktosun/nreup2010
Program Contacts:
Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473
Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470