Classification of Traveling Wave Solutions of Reaction-Diffusion Systems.
BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
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A classification scheme is presented for traveling wave solutions of reaction diffusion systems of the form x sub t x sub alpha alpha Del Vx where t, are elements of R x is an element of R superscript n and V R superscript n approaches R. The important assumptions on V are that the limit as the absolute value of x approaches infinity of Vx is minus infinity, that the set xbarVx - Q is convex for Q sufficiently large that V has a finite number of critical points, and that if M sub 1 and M sub 2 are critical points of V then VM sub 1 not equal VM sub 2. The primary tools used are the Conley index and connection matrix. The classifications are given via paths in graphs whose vertices and edges are connection matrices. These results are then used to prove the existence of an infinite number of traveling wave solutions for a specific example.
- Theoretical Mathematics