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arXiv · 1201.2863

Unstable gap solitons in inhomogeneous Schrodinger equations

R. Marangell·H. Susanto·C. K. R. T. Jones
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Abstract

A periodically inhomogeneous Schrodinger equation is considered. The inhomogeneity is reflected through a non-uniform coefficient of the linear and non-linear term in the equation. Due to the periodic inhomogeneity of the linear term, the system may admit spectral bands. When the oscillation frequency of a localized solution resides in one of the finite band gaps, the solution is a gap soliton, characterized by the presence of infinitely many zeros in the spatial profile of the soliton. Recently, how to construct such gap solitons through a composite phase portrait is shown. By exploiting the phase-space method and combining it with the application of a topological argument, it is shown that the instability of a gap soliton can be described by the phase portrait of the solution. Surface gap solitons at the interface between a periodic inhomogeneous and a homogeneous medium are also discussed. Numerical calculations are presented accompanying the analytical results.

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R. Marangell, H. Susanto, C. K. R. T. Jones. 2012-01-13. Unstable gap solitons in inhomogeneous Schrodinger equations. https://arxiv.org/abs/1201.2863

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