A novel non-isospectral hierarchy and soliton wave dynamics for a parity-time-symmetric nonlocal vector nonlinear Gross–Pitaevskii equations

Abstract

Starting from a non-isospectral problem, we derive a hierarchy of nonlocal vector Gross-Pitaevskii (NVGP) equations with space-time external potential, which includes the nonlocal vector nonlinear Schrödinger (NVNLS) equation with self-induced PT-symmetric potential. In particular, we study the solutions with PT-symmetric potential for NVGP equations. Then, we obtain some novel non-autonomous breather solutions, quasi-rogue wave solutions and rational waves of NVGP equations via similarity and Darboux methods, and consider some controllable behaviors of these non-autonomous wave solutions. The obtained results are different form the local case, the NVGP equations with PT-symmetry have not the rogue wave solutions, but there are some quasi-rogue wave solutions and rational waves in this system. Furthermore, some properties of the non-autonomous rational(NR) waves are investigated analytically for the NVGP equations, and the dynamical stabilities of the NR solutions are derived through the numerical method. Some propagation phenomena are produced through manipulating non-autonomous waves, which can present the potential applications to the wave phenomena in nonlocal wave models, nonlinear optics and condensed matter physics.