Abstract
Abstract In this article, the sine-Gordon expansion method is employed to find some new traveling wave solutions to the nonlinear Schrödinger equation with the coefficients of both group velocity dispersion and second-order spatiotemporal dispersion. The nonlinear model is reduced to an ordinary differential equation by introducing an intelligible wave transformation. A set of new exact solutions are observed corresponding to various parameters. These novel soliton solutions are depicted in figures, revealing the new physical behavior of the acquired solutions. The method proves its ability to provide good new approximate solutions with some applications in science. Moreover, the associated solution of the presented method can be extended to solve more complex models.
Highlights
In this article, the sine-Gordon expansion method is employed to find some new traveling wave solutions to the nonlinear Schrödinger equation with the coefficients of both group velocity dispersion and second-order spatiotemporal dispersion
Some new traveling wave solutions are found while changing the values of the parameters
The proposed method is shown to provide a solution with important physical representation which may help in dealing with similar complex nonlinear models with applications in contemporary science and other related areas
Summary
Abstract: In this article, the sine-Gordon expansion method is employed to find some new traveling wave solutions to the nonlinear Schrödinger equation with the coefficients of both group velocity dispersion and second-order spatiotemporal dispersion. Many numerical and analytical approaches are being developed such as the auxiliary equation method [31], Cole-Hopf transformation, exp-function method [32], sine-cosine method [33], Darboux transformation [34], Hirota method [35], Lie group analysis [36], modified simple equation method [37], similarity reduced method, tanh method, inverse scattering scheme [38], Bäcklund transform method [39], homogeneous balance scheme [40], sine-cosine method, tanh-coth method, extended FAN sub-equation method [41], auxiliary equation method [42], and many more One of these important and effective methods that may provide good solutions with important physical behaviors is the sine-Gordon expansion method.
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