Dark and new travelling wave solutions to the nonlinear evolution equation

Abstract

Obtaining new and important travelling wave solutions of wave propagation modelling of waves such as nonlinear optics models, propagation and transmission models of waves by using different methods plays an important role in maritime engineering, ocean, beach science and floating structures, and also for understanding new physical meanings of coastal structural properties. New complex travelling wave solutions obtained by using different newly improved methods explain new and general properties of nonlinear optic structures, wave propagations and motions, major structures of the impact of environmental factors on the beach like tsunami, the impact of the waves on the vessel, the power of the effects of the waves on wave distribution panels. These solutions structures may be trigonometric, complex function, hyperbolic function, exponential and rational function. In this study, we apply two effective methods to the nonlinear evolution equation used to describe the new versions of different mathematical models for wave motion and propagations. The first is improved Bernoulli sub-equation function method (IBSEFM), the latter is modified exp(-Ω(ξ))-expansion function method (MEFM). We obtain some new travelling wave structures such as complex function, hyperbolic function and rational function, exponential function solutions. We observe that all travelling wave solutions have been verified the nonlinear partial differential equation by using Wolfram Mathematica 9. Then, we plot the two and three dimensional surfaces for all travelling wave structures obtained in this paper by the same computer program.