Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Infinitely many traveling wave solutions of a gradient system

Author: David Terman
Journal: Trans. Amer. Math. Soc. 301 (1987), 537-556
MSC: Primary 35K55; Secondary 35B99
MathSciNet review: 882703
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Abstract: We consider a system of equations of the form $ {u_t} = {u_{xx}} + \nabla F(u)$. A traveling wave solution of this system is one of the form $ u(x,\,t) = U(z),\,z = x + \theta t$. Sufficient conditions on $ F(u)$ are given to guarantee the existence of infinitely many traveling wave solutions.

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Article copyright: © Copyright 1987 American Mathematical Society