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Transactions of the American Mathematical Society

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

 

 

Traveling wave solutions of a gradient system: solutions with a prescribed winding number. II


Author: David Terman
Journal: Trans. Amer. Math. Soc. 308 (1988), 391-412
MSC: Primary 35K57; Secondary 20E05, 35B99
Part I: Trans. Amer. Math. Soc. (1) (1988), 369-389
MathSciNet review: 946449
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Abstract: This paper completes the analysis begun in [2] concerning the existence of traveling wave solutions of a system of the form $ {u_t} = {u_{xx}} + \nabla F(u)$, $ u \in {{\mathbf{R}}^2}$. In [2] a notion of winding number for solutions was defined, and the proof that there exists a traveling wave solution with a prescribed winding number was reduced to a purely algebraic problem. In this paper the algebraic problem is solved.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0946449-9
Article copyright: © Copyright 1988 American Mathematical Society