The surface solitons in media with uniform and Gaussian modulated potentials

We investigate the existence and stability of solitons in media with uniform and Gaussian modulated potentials, including linear case, and self-focusing and self-defocusing nonlinear cases. For linear case, the eigenvalues and eigenfunction for different modulated depths of Gaussian potentials are obtained numerically. For nonlinear cases, the existence and stability of fundamental and multipole solitons are studied in self-focusing and self-defocusing media. For a fixed modulated depth, the eigenvalue for fundamental or multipole linear modes is equal to the critical propagation constant bc of fundamental and multipole solitons existence. Fundamental solitons are stable in both the self-defocusing nonlinear media and the self-focusing nonlinear case. Multipole solitons are stable with the propagation constants close to bc both for self-focusing and self-defocusing nonlinearities.