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Bifurcation analysis of stationary solutions of two-dimensional coupled Gross–Pitaevskii equations using deflated continuation

Accepted version
Peer-reviewed

Type

Article

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Authors

Farrell, PE 
Kevrekidis, PG 

Abstract

Recently, a novel bifurcation technique known as deflated continuation was applied to the single-component nonlinear Schrödinger (NLS) equation with a parabolic trap in two spatial dimensions. This bifurcation analysis revealed previously unknown solutions, shedding light on this fundamental problem in the physics of ultracold atoms. In the present work, we take this a step further by applying deflated continuation to two coupled NLS equations, which – feature a considerably more complex landscape of solutions. Upon identifying branches of solutions, we construct the relevant bifurcation diagrams and perform spectral stability analysis to identify parametric regimes of stability and instability and to understand the mechanisms by which these branches emerge. The method reveals a remarkable wealth of solutions. These include both well-known states arising from the Cartesian and polar small amplitude limits of the underlying linear problem, but also a significant number of more complex states that arise through (typically pitchfork) bifurcations.

Description

Keywords

4901 Applied Mathematics, 4903 Numerical and Computational Mathematics, 49 Mathematical Sciences

Journal Title

Communications in Nonlinear Science and Numerical Simulation

Conference Name

Journal ISSN

1007-5704
1878-7274

Volume Title

87

Publisher

Elsevier BV