Remote Access Transactions of the American Mathematical Society
Green Open Access

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. I


Author: David Terman
Journal: Trans. Amer. Math. Soc. 308 (1988), 369-389
MSC: Primary 35K57; Secondary 20E05, 35B99
DOI: https://doi.org/10.1090/S0002-9947-1988-99924-9
Part II: Trans. Amer. Math. Soc. (1) (1988), 391-412
MathSciNet review: 946449
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Consideration is given to a system of equations of the form $ {u_t} = {u_{xx}} + \nabla F(u)$, $ u \in {{\mathbf{R}}^2}$. In a previous paper [6], conditions of $ F$ were given which guarantee that the system possesses infinitely many traveling wave solutions. The solutions are now characterized by how many times they wind around in phase space. A winding number for solutions is defined. It is demonstrated that for each positive integer $ K$, there exists at least two traveling wave solutions, each with winding number $ K$ or $ K + 1$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35K57, 20E05, 35B99

Retrieve articles in all journals with MSC: 35K57, 20E05, 35B99


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-99924-9
Article copyright: © Copyright 1988 American Mathematical Society