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A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation. (English) Zbl 0862.34030
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:
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C25Periodic solutions of ODE
35Q35PDEs in connection with fluid mechanics
34C37Homoclinic and heteroclinic solutions of ODE