Theoretical Mathematics & Applications

The sub-equation method and new travelling wave analytical solutions of nonlinear Schrödinger's equation with Kerr law nonlinearity

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• Abstract

  In this paper we construct new travelling wave solutions to the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity by introducing the sub-equation method and the generalized Riccati equation. The travelling wave solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. We also discuss the reliability of the proposed method and compared the obtained solutions with those previously reported in the literature. The presented method provides a comprehensive approach to construct many new solutions for nonlinear partial differential equations.