The solitons in Bessel lattice potential with nonlocal nonlinearity

The existence and stability of fundamental and multipole solitons in Bessel potential are studied, including linear case, and nonlocal nonlinearity cases. For linear case, the eigenvalues and eigenfunction for different modulated depths of Bessel potential are obtained numerically. For nonlocal nonlinear cases, the existence and stability of fundamental and multipole solitons are studied. The results show that there exists a critical propagation constant b _c of solitons, below which the solitons vanish. The value of b _c is associated with the eigenvalue for linear case. It is found that nonlocality can expand the stability region of solitons. Fundamental and dipole solitons are stable in the whole region and the stable range of multipole solitons increase with increasing of the nonlocal degree.