The Properties of the Solutions of Nonlinear Schrödinger Equation with Center Potential

Abstract The solutions of a nonlinear Schrödinger equation containing the nonlinear interaction b|ϕ|2 ϕ and center potential are found using the new method of separation of functions, in which the two wave functions satisfy the soluble and different equations, respectively. Its solution is still a soliton, which possesses both corpuscle and wave feature, its eigenenergy is still determinant and quantized, but its size of eigenenergy is depressed about A 0′2 b/2 relative to that in linear case. This means that the localized nature of the particles described by the nonlinear Schrödinger equation with a center potential is enhanced due to the nonlinear interaction. This is first time to obtain the soliton solution of the nonlinear Schrödinger equation, which has an important significance and application in the nonlinear science, physics, chemistry, biology and engineering.