New Solutions for the Higher-Order Nonlinear Schr dinger Equation Using Integral Methods

In this paper, we use two integral methods, the first integral method and the direct integral method to study a higher-order nonlinear Schr dinger equation (NLSE). The application of the first integral method yield trigonometric function solutions and solitary wave solutions. Using the direct integration lead to shock wave solution and Jacobi elliptic function solutions. The direct integral method is more concise and direct than the first integral method.