Unstaggeredstaggered solitons on one and twodimensional twocomponent discrete nonlinear Schrödinger lattices
Abstract
We study coupled unstaggeredstaggered soliton pairs emergent from a system of two coupled discrete nonlinear Schrödinger (DNLS) equations with the selfattractive onsite selfphasemodulation nonlinearity, coupled by the repulsive crossphasemodulation interaction, on 1D and 2D lattice domains. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. While most work on DNLS systems addressed symmetric onsitecentered fundamental solitons, these models give rise to a variety of other excited states, which may also be stable. The simplest among them are antisymmetric states in the form of discrete twisted solitons, which have no counterparts in the continuum limit. In the extension to 2D lattice domains, a natural counterpart of the twisted states are vortical solitons. We first introduce a variational approximation (VA) for the solitons, and then correct it numerically to construct exact stationary solutions, which are then used as initial conditions for simulations to check if the stationary states persist under time evolution. Twocomponent solutions obtained include (i) 1D fundamentaltwisted and twistedtwisted soliton pairs, (ii) 2D fundamentalfundamental soliton pairs, and (iii) 2D vorticalvortical soliton pairs. We also highlight a variety of other transient dynamical regimes, such as breathers and amplitude death. The findings apply to modeling binary BoseEinstein condensates, loaded in a deep lattice potential, with identical or different atomic masses of the two components, and arrays of bimodal optical waveguides.
 Publication:

Communications in Nonlinear Science and Numerical Simulations
 Pub Date:
 June 2020
 DOI:
 10.1016/j.cnsns.2020.105244
 Bibcode:
 2020CNSNS..8505244V
 Keywords:

 Discrete nonlinear Schrödinger equations;
 Unstaggeredstaggered lattice;
 Variational approximation;
 Solitons