We introduce an exactly integrable nonlinear model describing the dynamics of spinor solitons in space-dependent matrix gauge potentials of rather general types. The model is shown to be gauge equivalent to the integrable system of vector nonlinear Schrödinger equations known as the Manakov model. As an example we consider a self-attractive Bose-Einstein condensate with random spin-orbit coupling (SOC). If Zeeman splitting is also included, the system becomes nonintegrable. We illustrate this by considering the random walk of a soliton in a disordered SOC landscape. While at zero Zeeman splitting the soliton moves without scattering along linear trajectories in the random SOC landscape, at nonzero splitting it exhibits strong scattering by the SOC inhomogeneities. For a large Zeeman splitting the integrability is recovered. In this sense the Zeeman splitting serves as a parameter controlling the crossover between two different integrable limits.
Thermalization of Weakly Nonintegrable FPUT and Toda Dynamics: A Lyapunov Spectrum Perspective
Center for Theoretical Physics of Complex Systems, Institute for Basic Science（复杂系统理论物理中心，基础科学研究所）；Department of Physics, Pukyong National University（釜庆国立大学物理系）；Basic Science Program, Korea University of Science and Technology (UST)（韩国科学技术院基础科学项目）；Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study (NZIAS), Massey University Albany（梅西大学奥克兰分校新西兰高级研究院理论与化学物理中心）
Lax Pairs: Integrable, Less Integrable and Nonintegrable Systems
National and Kapodistrian University of Athens（雅典国立卡波季斯特里安大学）；University of Crete（克里特大学）；Institute of Applied and Computational Mathematics, FORTH（应用与计算数学研究所，FORTH）
Minimal nonintegrable models with three-site interactions
School of Physics, Northwest University（西北大学物理学院）；Institute of Modern Physics, Northwest University（西北大学现代物理研究所）；Shaanxi Key Laboratory for Theoretical Physics Frontiers（陕西理论物理前沿重点实验室）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）；Fundamental Discipline Research Center for Quantum Science and Technology of Shaanxi Province（陕西省量子科学与技术基础学科研究中心）
