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NREUP 2009

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

Dummy View - NOT TO BE DELETED