New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation

Mustafa Inc,Muhammad Nasir Ali,E A Az-Zo’Bi,Adil Jhangeer,Mohammed K A Kaabar,Hadi Rezazadeh

doi:10.1515/nleng-2021-0029

Abstract

Abstract In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are also described graphically while taking suitable values of free parameters. The applied algorithms are effective and convenient in handling the solution process for Ito equation that appears in many phenomena.

Highlights

In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions
Three classes of traveling-wave solutions for the nonlocal (2+1) Ito equation have been explored via the simplest equation algorithm (SEM) and modi ed simplest equation algorithm (MSEM)
Using SEM along using of Bernoulli equation produced bright solitons provided in Eqs. (3.11)-(3.15)

Summary

Introduction

Abstract: In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modi ed simplest equation algorithms are utilized to nd exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are described graphically while taking suitable values of free parameters. The applied algorithms are e ective and convenient in handling the solution process for Ito equation that appears in many phenomena. Numerous complex phenomena that are encountered in mathematical physics, relativity, and economics are modeled via nonlinear di erential equations [1]. Several techniques have been introduced to construct exact solutions for NLEEs in the last few decades. Various e ective techniques have been proposed. ( /G )-expansion algorithm [2], bifurcation method [3], Hirota bilinear approach [4], sine-cosine method [5], Adomian decomposition algorithm and its

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The Method of Simplest Equation

Discussion and Conclusion