This article concerns the over-determined system of partial differential equations
It was shown in [6, Theorem 8.1] that this system with admits traveling wave solutions as well as non-traveling wave solutions. In this article we solve completely this system when . Our main result states that this system admits only traveling wave solutions, whenever .
Submitted December 1, 2011. Published May 23, 2012.
Math Subject Classifications: 35N05, 35C07, 35C99.
Key Words: Over-determined PDE system; traveling wave solution; exact solution; Hamiltonian stationary Lagrangian surfaces.
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| Bang-Yen Chen |
Department of Mathematics, Michigan State University
619 Red Cedar Road
East Lansing, Michigan 48824-1027, USA
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