Publication Date

2006

Journal or Book Title

PHYSICAL REVIEW E

Abstract

In this paper, we examine in detail the principal branches of solutions that arise in vector discrete models with nonlinear intercomponent coupling and four wave mixing. The relevant four branches of solutions consist of two single mode branches (transverse electric and transverse magnetic) and two mixed mode branches, involving both components (linearly polarized and elliptically polarized). These solutions are obtained explicitly and their stability is analyzed completely in the anticontinuum limit (where the nodes of the lattice are uncoupled), illustrating the supercritical pitchfork nature of the bifurcations that give rise to the latter two, respectively, from the former two. Then the branches are continued for finite coupling constructing a full two-parameter numerical bifurcation diagram of their existence. Relevant stability ranges and instability regimes are highlighted and, whenever unstable, the solutions are dynamically evolved through direct computations to monitor the development of the corresponding instabilities. Direct connections to the earlier experimental work of Meier et al. [Phys. Rev. Lett., 91, 143907 (2003)] that motivated the present work are given.

Comments

This is the pre-published version harvested from arXiv. The published version is located at http://pre.aps.org/abstract/PRE/v73/i6/e066601

Pages

-

Volume

73

Issue

6

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