Multi-pole solitons and breathers with spatially periodic modulation induced by the helicoidal spin-orbit coupling

TL;DR

This paper presents analytical and numerical studies of multi-pole solitons and breathers in spin-orbit coupled Bose-Einstein condensates, revealing how helicoidal SOC induces complex spatial patterns and dynamic behaviors.

Contribution

It introduces new analytical solutions for multi-pole solitons and breathers in inhomogeneous BECs with helicoidal SOC, highlighting their unique trajectories and stability properties.

Findings

Modulation effects induce stripe patterns in solitons.

Spatially periodic backgrounds for beating solitons and breathers.

Logarithmically increasing separation trajectories.

Abstract

We report analytical solutions for diverse multi-pole (MP) soliton and breather states in spatially inhomogeneous binary Bose-Einstein condensates (BECs) with the helicoidally shaped spin-orbit coupling (SOC), including MP stripe solitons on zero background, MP beating stripe solitons on a nonzero plane-wave background, as well as MP beating stripe solitons and MP breathers on periodic backgrounds. The results indicate that modulation effects produced by the helicoidal SOC not only induce stripe patterns in MP solitons, but also generate the spatially-periodic background for the MP beating stripe solitons and breathers. An asymptotic analysis reveals curved trajectories with a logarithmically increasing soliton/breather separation for these MP excitations, fundamentally distinguishing them from periodic trajectories of bound-state solitons/breathers or straight trajectories of conventional multi-soliton/breather sets. With complex periodic structures in individual components, the total density distribution is nonperiodic, due to their configurations which are out-of-phase with respect to the two components. We further examine several degenerate structures of MP solitons and breathers under varying SOC and spectral parameters. Numerical simulations validate the analytical results and demonstrate stability of these MP excitations. These findings may facilitate deeper understanding of soliton/breather interactions beyond conventional multi-soliton systems and bound-state complexes in SOC BEC.