Traveling wave solutions of a gradient system: solutions with a prescribed winding number. II
HTML articles powered by AMS MathViewer
- by David Terman PDF
- Trans. Amer. Math. Soc. 308 (1988), 391-412 Request permission
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.References
- David Terman, Infinitely many traveling wave solutions of a gradient system, Trans. Amer. Math. Soc. 301 (1987), no. 2, 537–556. MR 882703, DOI 10.1090/S0002-9947-1987-0882703-6
- David Terman, Traveling wave solutions of a gradient system: solutions with a prescribed winding number. I, II, Trans. Amer. Math. Soc. 308 (1988), no. 1, 369–389, 391–412. MR 946449, DOI 10.1090/S0002-9947-1988-99924-9
- D. Terman, Infinitely many radial solutions of an elliptic system, Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), no. 6, 549–604 (English, with French summary). MR 929475
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 308 (1988), 391-412
- MSC: Primary 35K57; Secondary 20E05, 35B99
- DOI: https://doi.org/10.1090/S0002-9947-1988-0946449-9
- MathSciNet review: 946449