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NREUP 2008

University of Texas at Arlington

Title: Solitons and Nonlinear Partial Differential Equations

Directors: Tuncay Aktosun and Minerva Cordero

Email: aktosun@uta.edu

Dates of Program: June 1 - July 19, 2008

Summary: Solitary wave solutions (soliton solutions) to four nonlinear partial differential equations (PDEs) are investigated and their applications in various areas are studied. These nonlinear PDEs 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, and the modified Korteweg-de Vries (mKdV) equation ut+6u2ux+uxxx=0. The goal is to obtain soliton solutions to these four equations in a systematic way and to derive the N-soliton solution formula for each equation. 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/nreup2008.

Student Researchers Supported by MAA:

  • Ernesto Garcia
  • Carolina Liskey
  • Carl Looney
  • Antonio Lopez
  • Crystal Red Eagle
  • Sam Rivera

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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