Exact solutions for the perturbed nonlinear Schrödinger equation with power law nonlinearity and Hamiltonian perturbed terms

Abstract

In this paper, we apply four mathematical methods, namely, the sine–cosine method, the Jacobi elliptic equation method, the generalized Kudryashov method and the Riccati equation method for constructing many new exact solutions, the bright, dark, singular soliton solutions, the symmetrical hyperbolic Fibonacci function solutions and the Jacobi elliptic function solutions with parameter of the perturbed nonlinear Schrödinger equation with power law nonlinearity and Hamiltonian perturbed terms. When the parameters take special values, the soliton and other solutions are derived from the exact solutions. The used methods in this paper present a wider applicability for handling nonlinear wave equations. Comparing our new results with the well-known results are given. Also, we compare between the results yielding from the above methods.