Approximate bright-soliton solution of the higher-order nonlinear Schrödinger equation

In this paper, approximate bright-soliton solutions of the higher-order nonlinear Schrödinger equation are constructed by treating the higher-order terms as small perturbations. The first-, second-, and third-order asymptotic solutions are obtained. The errors between the asymptotic solutions and the numerical/analytical solutions are discussed, which gives a high accuracy of the approximate solutions. It is pointed that the asymptotic solutions can be used as the initial value to improve the accuracy of the numerical solutions. This paper may be helpful for undergraduate and graduate students in mathematics and physics to understand the approximate soliton solutions of the higher-order nonlinear Schrödinger equation.