Abstract
The focus of this work is to explore the macroscopic property of solitary waves in nonlocal nonlinear materials which extend to nonlinear optical systems and atomic optical systems. Nonlocal nonlinearity are known to improve the stability of solitary waves by reducing the nonlinear power. This work reveals insights to bifurcate behavior and instability nature of solitary waves in nonlocal nonlinearity in general aspects and in specific details. Nonlocal nonlinear response reduces the formation power a guided bright soliton in a dark-bright vector soliton pair, providing controllability over the band structure of scalar waves and enhence the mobility of wave packets in periodic potential; also the symmetry-breaking in- stabilities are remarkably suppressed ascribable to the fact that nonlocal response exhibits slow steady-state spatial response to the noise spectrum. Such a ”low pass filter” ’effect restricts the noise to grow in all the transverse dimensions and results in the reduction of the effective order of nonlinearity in the system. Furthermore, elliptical solitons in 2D nonlinear Schr"{o}dinger equations are proposed and studied numerically with a more generalized formulation showing the existence and symmetry-breaking instabilties of new families of solitons, vortices, and soliton rings with elliptical symmetry, which paves the way for future insvestigation of 2D nonlocal nonlinear system.