radiation. The study is carried out numerically, and basic results are explained by means of analytical considerations.'
author:
- 'Krzysztof B. Zegadlo$^{1}$, Nir Dror$^{2}$, Marek Trippenbach$^{3}$, Miroslaw A. Karpierz$^{1}$ and Boris A. Malomed$^{2}$'
title: 'Spontaneous symmetry breaking of self-trapped and leaky modes in quasi-double-well potentials'
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Introduction
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Usually, the ground state (GS) of quantum-mechanical systems exactly follows the symmetry of the underlying Hamiltonian [@LL], while excited states may realize different representations of the same symmetry (a different situation is exemplified by the Jahn-Teller effect in molecules, which makes the GS of the electron subsystem spatially asymmetric, thus breaking the symmetry of the respective Hamiltonian [@RE]). In particular, for the double-well potential (DWP), which is dealt with in the present work, the GS wave function is spatially even, while the first excited state is odd. This is not necessarily true in many-body settings. In that context, the mean-field description of atomic Bose-Einstein condensates (BECs) is provided by the Gross-Pitaevskii equation (GPE) [@BEC], which includes the cubic term accounting for attractive forces between colliding atoms. Essentially the same is the nonlinear Schrödinger equation (NLSE) modeling the propagation of optical signals in Kerr-nonlinear media [NLS]{}. If the self-focusing nonlinearity is strong enough, 