University of Texas at Arlington

Title: Exact Solutions to Nonlinear Evolution Equations

Directors:

Tuncay Aktosun
Minerva Cordero

Email:

aktosun@uta.edu

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 u_t-6uu_x+u_xxx=0, the nonlinear SchrÃ¶dinger (NLS) equation iu_t+u_xx+2|u|²u=0, the sine-Gordon equation u_xt=sinu, the modified Korteweg-de Vries (mKdV) equation u_t+6u²u_x+u_xxx=0, and the Toda lattice equation ’²u_n/’t² =e^-u_n+u_n-1-e^-u_n+1+u_n. 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.