Phase transition in a Rabi coupled two-component Bose–Einstein condensate

Aftalion, Amandine; Sourdis, Christos

doi:10.1016/j.na.2019.03.018

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“…We also refer to [1,3] for recent results regarding a system obtained from (1.1) adding in each equation an additional term representing the spin coupling.…”

Section: Introductionmentioning

confidence: 99%

Saddle-shaped positive solutions for elliptic systems with bistable nonlinearity

Soave

2020

Mathematics in Engineering

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In this paper we prove the existence of infinitely many saddle-shaped positive solutions for non-cooperative nonlinear elliptic systems with bistable nonlinearities in the phaseseparation regime. As an example, we prove that the systemhas infinitely many saddle-shape solutions in dimension 2 or higher. This is in sharp contrast with the case Λ ∈ (0, 1], for which, on the contrary, only constant solutions exist.

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“…We also refer to [1,3] for recent results regarding a system obtained from (1.1) adding in each equation an additional term representing the spin coupling.…”

Section: Introductionmentioning

confidence: 99%