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In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons.

All optical communications are being used for transcontinental and transoceanic data transfer, through long-haul optical fibers, at the present time. There are various aspects of soliton communication that still need to be addressed. One of the features is the dispersive optical solitons. In presence of higher order dispersion terms, soliton communications are sometimes a hindrance as these dispersion terms produce soliton radiation. Nonlinear evolution equations have a major role in various scientific and engineering fields, such as optical fibers. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction, and convection are very important in nonlinear wave equations. In recent years, quite a few methods for obtaining explicit traveling and solitary wave solutions of nonlinear evolution equations have been proposed. In recent years, exact homoclinic and heteroclinic solutions were proposed for some NEEs like nonlinear Schrödinger equation, Sine-Gordon equation, Davey-Stewartson equation, Zakharov equation, and Boussinesq equation [

In particular, the study of the coupled Schrödinger-Boussinesq equations has attracted much attention of mathematicians and physicists [

The nonlinear coupled Schrödinger-Boussinesq equation (SBE) governs the propagation of optical solitons in a dispersive optical fiber and is a very important equation in the area of theoretical and mathematical physics. This paper is going to take a look at the bright, dark, and singular soliton solutions for Kerr law nonlinearity media.

Consider the coupled Schrödinger-Boussinesq equations (SBE). They appeared in [

Consider the nonlinear partial differential equation in the form

The solutions of many nonlinear equations can be expressed in the following form.

We substitute (

The starting hypothesis for solving (

Substituting (

Seeking the solution by sech function method as in (

Figures

The solitary wave of the real part of

The solitary wave

Seeking the solution by tanh function method as in (

Figures

The solitary wave of the real part of

The solitary wave

Seeking the solution by sech function method as in (

Figures

The solitary wave of the real part of

The solitary wave of

This section will analyze (

In (

Then

Substitute (

And

In this paper the dispersive bright, dark, and singular soliton solutions to SBE with Kerr law of nonlinearity were studied. The sech, tanh, csch, and the modified simplest equation method have been successfully applied to find solitons solutions for the coupled Schrödinger-Boussinesq equations. Several constraint conditions were assuring the existence of such solitons with Kerr law nonlinearity. The modified simple equation method does not produce the soliton solution in general case. Solutions by three methods are plotted in figures for the real and imaginary parts for

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by Al-Rafidain University College.