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arXiv · 1702.00701

Orbital Stability of Domain Walls in Coupled Gross-Pitaevskii Systems

Andres Contreras·Dmitry E. Pelinovsky·Michael Plum
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Abstract

Domain walls are minimizers of energy for coupled one-dimensional Gross--Pitaevskii systems with nontrivial boundary conditions at infinity. It has been shown that these solutions are orbitally stable in the space of complex $\dot{H}^1$ functions with the same limits at infinity. In the present work we adopt a new weighted $H^1$ space to control perturbations of the domain walls and thus to obtain an improved orbital stability result. A major difficulty arises from the degeneracy of linearized operators at the domain walls and the lack of coercivity.

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Andres Contreras, Dmitry E. Pelinovsky, Michael Plum. 2017-02-02. Orbital Stability of Domain Walls in Coupled Gross-Pitaevskii Systems. https://arxiv.org/abs/1702.00701

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