Sub-ODE method and solitary wave solutions for higher order nonlinear Schrödinger equation

With the aid of an ordinary differential equation (ODE) involving an arbitrary positive power of dependent variable and its various positive solutions, three types of solitary wave solution of the higher order nonlinear Schrödinger equation (NLSE) with non-Kerr terms have been found out, which are the bell type solitary waves, the kink type solitary waves and the algebraic solitary waves, provided that the coefficients of the higher order NLSE satisfy certain constraint conditions.