Interactions among lump optical solitons for coupled nonlinear Schrödinger equation with variable coefficient via bilinear method.

In this paper, a non-autonomous (3+1) dimensional coupled nonlinear Schrödinger equation (NLSE) with variable coefficients in optical fiber communication is analyzed. By means of bilinear technique and symbolic computations, new multi-soliton solutions of the coupled model in different trigonometric and lump functions are given. Then, in terms of perturbed waves, considering the steady state solution and the small perturbation on the three directions x, y, z and the time t, the soliton transmission are also considered. The behaviour of interaction among lump periodic soliton is studied and optical soliton solutions are reached. This study has certain significance for the analysis of other nonlinear dispersion systems and the application of optical physics. The results are presented through graphs generated by using Maple. The important feature of the proposed study is to show different behaviour of the soliton at each component. The behaviour of solitons, their interactions, and their transformations are all governed by the fundamental concept of energy conservation in all three examples. We demonstrate the efficiency of our suggested methodology for analyzing the NLSE equations using the numerical simulations and analytical tools, yielding fresh insights into their behaviour and solutions. Our findings help to develop mathematical tools for investigating nonlinear partial differential equation (NLPDEs) and provide new insights on the dynamics of NLSE equations, which have implications for many domains of physics and applied mathematics.

Multiple rogue wave, double-periodic soliton and breather wave solutions for a generalized breaking soliton system in (3 + 1)-dimensions.

We focused on solitonic phenomena in wave propagation which was extracted from a generalized breaking soliton system in (3 + 1)-dimensions. The model describes the interaction phenomena between Riemann wave and long wave via two space variable in nonlinear media. Abundant double-periodic soliton, breather wave and the multiple rogue wave solutions to a generalized breaking soliton system by the Hirota bilinear form and a mixture of exponentials and trigonometric functions are presented. Periodic-soliton, breather wave and periodic are studied with the usage of symbolic computation. In addition, the symbolic computation and the applied methods for governing model are investigated. Through three-dimensional graph, density graph, and two-dimensional design using Maple, the physical features of double-periodic soliton and breather wave solutions are explained all right. The findings demonstrate the investigated model's broad variety of explicit solutions. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering.

Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas.

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail.

Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation.

Introduction: The multiple Exp-function scheme is employed for searching the multiple soliton solutions for the fractional generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky- Konopelchenko equation. Objectives: Moreover, the Hirota bilinear technique is utilized to detecting the lump and interaction with two stripe soliton solutions. Methods: The multiple Exp-function scheme and also, the semi-inverse variational principle will be used for the considered equation. Results: We have obtained more than twelve sets of solutions including a combination of two positive functions as polynomial and two exponential functions. The graphs for various fractional-order α are designed to contain three dimensional, density, and y-curves plots. Then, the classes of rogue waves-type solutions to the fractional generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky- Konopelchenko equation within the frame of the bilinear equation, is found. Conclusion: Finally, a direct method which is called the semi-inverse variational principle method was used to obtain solitary waves of this considered model. These results can help us better understand interesting physical phenomena and mechanism. The dynamical structures of these gained lump and its interaction soliton solutions are analyzed and indicated in graphs by choosing suitable amounts. The existence conditions are employed to discuss the available got solutions.

Conservation laws and exact solutions of the ( 3 + 1 ) -dimensional Jimbo-Miwa equation.

In this article, by using the Herman-Pole technique the conservation laws of the ( 3 + 1 ) - Jimbo-Miwa equation are obtained, and then by using the Lie symmetry analysis all of the geometric vector fields of this equation are given. Also, the non-classical symmetries of the Jimbo-Miwa equation have been determined by applying nonclassical schemes. Eventually, the ansatz solutions of the Jimbo-Miwa equations utilizing the tanh technique have been offered.