The solitons in parity-time symmetric mixed Bessel linear potential and modulated nonlinear lattices

The optical solitons in parity-time (PT) symmetric mixed Bessel linear potential and modulated nonlinear lattices are studied, including linear case, and self-focusing modulated nonlinear lattices׳ cases. For linear case, the PT-breaking points, the eigenvalues and eigenfunction for different modulated depths of PT symmetry Bessel complex potential, are obtained numerically. The eigenvalue for linear case is equal to the critical propagation constant bc of soliton existence. With increasing of the depth of the nonlinear lattices, the power of fundamental solitons decreases and the beam width changes little, but the power of multipole solitons increases and the beam width decreases. Fundamental solitons are stable in the whole region and multipole solitons are stable with the propagation constants close to bc. The range of multipole solitons stability decreases with increasing of the depth of the nonlinear lattices.