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Exponential decay and blow up of a solution for a system of nonlinear higher-order wave equations AIP Conf. Proc. 1470, 118 (2012); 10.1063/1.4747654Landau-Lifshitz and higherorder nonlinear systems gauge generated from nonlinear Schrödingertype equations A set of coupled higher-order nonlinear Schrodinger equations, which describe electromagnetic pulse propagation in coupled optical waveguides, is formulated in terms of an eigenvalue problem. Using that result, the inverse scattering problem is solved and explicit soliton solutions are found. Additionally, linear coupling terms are studied systematically.1208

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We describe modulational instability (MI) of the continuous-wave (cw) states in the dual-core nonlinear optical ¢ber with normal dispersion.We show that the asymmetric cw states (existing above the bifurcation point), as well as the symmetric ones (below the bifurcation point) exhibit MI at all values of the intensity (the instability of the symmetric cw states was known previously).Below the bifurcation, the MI's peak gain (with respect to the perturbation frequency, holding the intensity of the symmetric cw state constant) increases with intensity. Above the bifurcation^considering the asymmetric cw sol-ution^the peak gain of this branch of the perturbation decreases with intensity; however, at the bifurcation point another branch goes unstable, its peak gain growing with intensity, and saturating at large intensities. The symmetric state's instability is non-oscillatory, while that of the asymmetric state is oscillatory. Direct simulations show that, in either case, MI eventually leads to full``optical turbulence,'' both the initial symmetric and initial asymmetric cw states giving rise to statistically symmetric turbulent states, which have equal average intensities in each core. Thus, the transition to turbulence restores the spontaneously broken symmetry.Ã Current