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In this work, we investigate various types of solutions for the generalised resonant dispersive nonlinear Schrödinger equation (GRD-NLSE) with power law nonlinearity. Based on simple mathematical techniques, the complicated form of the GRD-NLSE is reduced to an ordinary differential equation (ODE) which has a variety of solutions. The analytic solution of the resulting ODE gives rise to bright soliton, singular soliton, peaked soliton, compacton solutions, solitary pattern solutions, rational solution, Weierstrass elliptic periodic type solutions, and some other types of solutions. Constraint conditions for the existence of solitons and other solutions are given.

Solitons have become one of the more attractive topics in the physical and natural science. The reason of this remarkable importance is that this type of nonlinear waves has many applications in the study of nonlinear optics, plasma physics, fluid dynamics, and several other disciplines [

The formation of solitons in nonlinear optics, for example, is mainly due to a delicate balance between dispersion and nonlinearity in a model of NLSE. To analyse the dynamics of solitons, it is worthwhile to focus deeply on one model of the NLS family of equations with higher order nonlinear terms. There are many powerful mathematical tools that have been developed to study the behaviour of solitons in a medium dominated by NLSE. For more details, see [

The model of GRD-NLSE which is studied in the current paper has the form

In this paper, we aim to investigate the solitons and other types of solutions to GRD-NLSE. To achieve our goal, simple integration schemes will be applied to reduce the complicated form of GRD-NLSE to an ODE possessing various types of solutions. Solving the resulting ODE yields different physical structures of solutions for GRD-NLSE such as bright soliton, singular soliton, peaked soliton, compacton solutions, solitary pattern solutions, rational solution, Weierstrass elliptic periodic type solutions, and some other types of solutions.

In the following section, (

In order to deal with the complicated form of the GRD-NLSE given by (

Here, we aim to obtain the solitary wave solution of (

In this subsection, we intend to find the peaked soliton of (

Next, replacing the constant

In order to obtain compacton and solitary patterns solutions of (

In case of

Now, we aim to extract more types of solutions to (

In case of

The solution to (

The solution to (

The solution to (

The solution to (

The solution to (

Overall, the majority of results obtained here for (

It should be noted that the proposed transformation in (

This study scoped different physical structures of solutions for GRD-NLSE with power law nonlinearity. Applying a simple mathematical scheme allowed us to simplify the complex form of GRD-NLSE to an ODE. It is found that the constructed ODE is rich in various types of solitons and other solutions for GRD-NLSE. The derived solutions include bright soliton, singular soliton, peaked soliton, compacton solutions, solitary pattern solutions, rational solution, trigonometric function solutions, and Weierstrass elliptic periodic type solutions. All generated solutions are verified by utilising symbolic computation. The results obtained here can be useful to understand the physics of nonlinear optical fibers.

No data were used to support this study.

The author declares no conflicts of interest.