Analytical Traveling Wave and Soliton Solutions of the $$(2+1)$$ Dimensional Generalized Burgers–Huxley Equation

Leta, Temesgen Desta; Liu, Wenjun; Rezazadeh, Hadi; Ding, Jian; Achab, Abdelfattah El

doi:10.1007/s12346-021-00528-z

Cited by 10 publications

(3 citation statements)

References 24 publications

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“…In this modern era of research, finding soliton solutions is an important field to describe the physical behavior of the nonlinear PDEs. There are many different techniques to find the soliton solutions such as G /G expansion method https://www.journals.vu.lt/nonlinear-analysis [4,31], first integral method [5], Kudryashov method [3,8], generalized logistic equation method [22,34], Riccati mapping method [2,33], φ 6 -model expansion method [27,35], He's variational method [20], generalized exponential rational function method [12], Hirota bilinear method [11], modified exponential rational functional method [1], a new auxiliary equation [28], Riccati-Bernoulli sub-ODE method [7,16,19], etc. But in this study, we apply the new modified extended direct algebraic method and the existence of the solutions on the bistable Allen-Cahn equation with quartic potential.…”

Section: Introductionmentioning

confidence: 99%

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Analysis and soliton solutions of biofilm model by new extended direct algebraic method

Iqbal¹,

İnç

Sohail

et al. 2023

NAMC

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In this paper, the examination of soliton solutions of the biofilm model with the help of a new extended direct algebraic method is expressed. Besides the exact solutions, the existence of these solutions is also discussed with the help of the Schauder fixed point theorem. The nonlinear dynamical biofilm model which we consider in this paper is basically the bistable Allen–Cahn equation with quartic potential. For more physical understanding, the 3D plots of the solutions are presented. The different types of hyperbolic, trigonometric, and rational soliton solutions are gained. In the biofilm model, different parameters belong to certain spaces and give the exact solutions by applying the technique of new extended direct algebraic method. Exact solutions of the biofilm model are highlighted along with their restriction.

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Section: Introductionmentioning

confidence: 99%

“…These microbes consist of bacteria, fungi, algae, etc. ; see [14][15][16][17][18][19][20][21][22][23][24]. So, these results are new and affected in the living reproducing microbes that penchant to live in colonies form a biofilm.…”

Section: Introductionmentioning

confidence: 99%

Analysis and soliton solutions of biofilm model by new extended direct algebraic method

Iqbal¹,

İnç

Sohail

et al. 2023

NAMC

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“…The authors in an earlier study 34 have used the new auxiliary equation method II of this paper with

{\tau}_0&#x0003D;{\tau}_1&#x0003D;{\tau}_3&#x0003D;{\tau}_5&#x0003D;0

, to derive the solutions of the conformable fractional resonant Schrödinger equation. By a variety of approaches as the modified Kudryashov, the Riccati–Bernoulli sub‐ODE, and the bifurcation methods, the authors 35 have constructed the exact solutions of a nonlinear (2+1)‐dimensional generalized Huxley equation in inhomogeneous dispersive medium. Other important studies have been performed in previous studies 36,37 .…”

Section: Introductionmentioning

confidence: 99%

A variety of new soliton structures and various dynamical behaviors of a discrete electrical lattice with nonlinear dispersion via variety of analytical architectures

El‐Ganaini

Kumar²

2022

Math Methods in App Sciences

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Funding informationThere are no funders to report for this submission.Nonlinear electrical lattices are powerful experimental tool for studying nonlinear dispersive media and creating opportunities for the realistic modeling of electrical solitons. In this work, we adopt the generalized auxiliary equation methods, the first integral method, and the Möbius transformation approach to extract a variety of traveling and solitary wave solutions of the nonlinear Salerno equation describing the nonlinear discrete electrical lattice with nonlinear dispersion. The kink, antikink, dark, bright, peakons, antipeakons, and periodic wave solutions are all derived. The existence criteria of solitons are described. It has been shown that for the selective values of arbitrary constants in an auxiliary equation, the generalized auxiliary equation method II is reduced to the new 𝜙 6 -model expansion method as well as the new extended auxiliary equation method. The impact of free parameters on the obtained solutions is investigated and graphically depicted using physical descriptions. The acquired results are important for the validity of numerical and experimental results and further understanding of the wave propagation in the nonlinear discrete electrical lattice. In addition, the stability analysis of the obtained solitary wave solutions is studied. Furthermore, using the maple software, all derived solutions were checked by re-entering them into the considered equation.

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Auto-Bäcklund Transformation, Similarity Reductions and Solitons of an Extended ($$2+1$$)-Dimensional Coupled Burgers System in Fluid Mechanics

Gao¹,

Guo²,

Shan³

2022

Qual. Theory Dyn. Syst.

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Analytical Traveling Wave and Soliton Solutions of the $$(2+1)$$ Dimensional Generalized Burgers–Huxley Equation

Cited by 10 publications

References 24 publications

Analysis and soliton solutions of biofilm model by new extended direct algebraic method

Analysis and soliton solutions of biofilm model by new extended direct algebraic method

A variety of new soliton structures and various dynamical behaviors of a discrete electrical lattice with nonlinear dispersion via variety of analytical architectures

Auto-Bäcklund Transformation, Similarity Reductions and Solitons of an Extended ($$2+1$$)-Dimensional Coupled Burgers System in Fluid Mechanics

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