Uniqueness of the stationary wave for theExtended


The extended Fisher Kolmogorov equation, u t = ?u xxxx + u xx +u?u 3 , > 0, models a binary system near the Lifshitz critical point and is known to exhibit a stationary heteroclinic solution joining the equilibria 1. For the classical case, = 0, the heteroclinic is u(x) = tanh(x= p 2) and is unique up to the obvious symmetries. We prove the conjecture that the uniqueness persists all the way to = 1=8, where the onset of spatial chaos associated with the loss of monotonicity of the stationary wave is known to occur. Our methods are non-perturbative and employ a global cross-section to the Hamiltonian ow of the stationary fourth order equation on the energy level of 1. We also prove uniform a priori bounds on all bounded stationary solutions, valid for any > 0.

Cite this paper

@inproceedings{Kwapisz1997UniquenessOT, title={Uniqueness of the stationary wave for theExtended}, author={Jaroslaw Kwapisz}, year={1997} }