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NREUP 2007

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 p�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

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