A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation. (English) Zbl 0862.34030

Peletier, L. A.; Troy, W. C.

Topol. Methods Nonlinear Anal. 6, No. 2, 331-355 (1995).

For the extended Fisher-Kolmogorov equation, the authors develop a topological shooting method and apply it to prove the existence of a countably infinite number of kinks or heteroclinic orbits connecting the stable states. The discussion is made according to a critical value of the positive (constant) coefficient of the fourth order term of the equation. (When this coefficient is zero, the equation reduces to the Fisher-Kolmogorov one).

Reviewer: C.Popa (Iaşi)

MSC:

34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C25	Periodic solutions to ordinary differential equations
35Q35	PDEs in connection with fluid mechanics
34C37	Homoclinic and heteroclinic solutions to ordinary differential equations

Keywords:

extension Fisher-Kolmogorov equation; heteroclinic orbits