An investigation of the physical dynamics of a traveling wave solution called a bright soliton

Abstract

This study examines the 1 + 2 -dimensional Zoomeron equation, which has recently become popular in applied mathematics and physics. Bright soliton (non-topological), kink wave solution and traveling wave solutions are generated with the advantages of the generalized exponential rational function method. With the help of this method, it is aimed to produce different types of solutions for the Zoomeron equation compared to other traditional exponential function methods. The effects of parameters on the amplitude of the wave function are discussed, along with physical explanations backed by simulations. In addition, the advantages and disadvantages of the method for the 1 + 2 -dimensional Zoomeron equation are discussed.

Complexiton solutions, kink soliton and breather-wave solutions for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation

“…In the last few years, many scholars have studied equation (1) by using different methods. For example, Ma et al researched the exact solutions of equation (1) by means of the Hirota bilinear method [20] and Feng et al obtained resonant multi-soliton solutions of equation (1) with the help of the linear superposition principle [21]. Different from former researches, we apply two Auto-Bäcklund transformations and extended rational function method to obtain hyperbolic solutions and complexiton solutions in this work.…”

“…Then in section 3, we apply the extended transformed rational function method to find complexiton solutions. In section 4, we derive one-kink and two-kink soliton solutions for equation (1) with the help of Maple. In section 5, based on the extended homoclinic test approach, we get the breather-wave solution of equation (1).…”

“…Over the past few decades, the research of nonlinear evolution equations (NLEEs) which are important model in the field of engineer technology and natural science has made much exciting progress in related fields, such as fluid mechanics, oceanography, condense matter physics and plasma physics [1][2][3]. NlEEs have already played a crucial role in different fields of science on account of their extensive application.…”

A study on the solutions of (1+1)-dimensional Mikhailov-Novikov-Wang equation

“…® Received: [17]. This study, which was prepared to specify the solutions of the (1+1)-dimensional MNWIE using GERFM [18,19,20,21,22,23] was designed as follows: In Section 2, GERFM's basic principles are presented. In Section 3, some solutions of (1+1)-dimensional MNWIE have been obtained by applying GERFM.…”

Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

“…Te nonlinear evolution (1) has wide applications in optics, fuid dynamics, and fnance. Note that some kink wave solutions and travelling wave solutions have also been generated for the Zoomeron equation, which has a similar form as (1) [34]. Te trial function method, tanh expansion method, and direct perturbation method have been explored to get the exact solutions of the Ivancevic option pricing model.…”