Spatial Solitons of the Nonlinear Schrödinger Equation of Arbitrary Nonlinearity with a Potential Hill

Abstract

In this paper we report on time-independent localized solutions of the nonlinear Schrödinger equation of arbitrary nonlinearity with a potential:

$$\psi ,_{kk} = [1 - u(\vec x)]\psi - |\psi |^{2\sigma } \psi ,$$

(1)

where x _k are the spatial coordinates in normalized units, $u(\vec x)$ is the potential, u(r → ∞) → 0, r ²=x _k x _k , σ > 0. The equation is widely used in physics (for example, in nonlinear and integrated optics) in classical field theory, etc.