Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions

Iqbal, Muhammad Sajid; Seadawy, Aly R.; Baber, Muhammad Zafarullah; Qasim, Muhammad

doi:10.1016/j.chaos.2022.112600

Cited by 44 publications

(9 citation statements)

References 32 publications

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“…In this section, we initiate our investigation by considering the soliton solution of order one for equation (5), as outlined in [3]. The constraint condition takes the following form:…”

Section: First Order Solitonmentioning

confidence: 99%

“…This section introduces the assumption of  in a suitable manner to derive the fourth-order soliton solution for the proposed equation (5). To achieve this, we consider  as expressed below:…”

Section: Fourth Order Solitary Waves With Fissionmentioning

confidence: 99%

“…Various researchers have introduced numerous analytical approaches to attain solitary waves solutions. Some of them are listed in [4][5][6][7][8][9]. Among these, HB method is crucial one and has been used for analyzing more complex dynamics of solitons of integrable systems.…”

Section: Introduction and Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

Saifullah,

Ahmad,

Ali Khan

et al. 2024

Phys. Scr.

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The potential Kadomtsev-Petviashvili (pKP) equation delineates the development of small-amplitude, nonlinear, long waves characterized by a gradual variation in the transverse coordinate. The B-type KP equation outlines the relationships among exponentially localized shapes and was employed as a representation for shallow water waves and plasma physics. In this paper, we consider the combined pKP-BKP integrable equation. We discuss the multiple solitons of a newly proposed (3+1)-dimensional combined pKP-BKP integrable equation. We use the Hirota bilinear (HB) form of the considered equation to deduce fission process in higher order solitons with different orders. Moreover, the breather dynamics and its interaction with other solitons are investigated via HB. The lump solution and its interaction with first order and fourth order kink soliton is studied.

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“…In this section, we initiate our investigation by considering the soliton solution of order one for equation (5), as outlined in [3]. The constraint condition takes the following form:…”

Section: First Order Solitonmentioning

confidence: 99%

Section: Fourth Order Solitary Waves With Fissionmentioning

confidence: 99%

See 1 more Smart Citation

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

Saifullah,

Ahmad,

Ali Khan

et al. 2024

Phys. Scr.

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show abstract

“…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%

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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“…Various physical phenomena can be formulated by a set of equations that help to understand and predict future events. In the past twenty years, partial differential equations (PDEs) have been used to study a wide range of natural phenomena 1 – 5 . The flow of fluids with fissured rock, thermodynamics, finance, ecology, mathematical physics, soil mechanics, and heat conduction difficulties in diverse materials are some of the disciplines where nonlinear PDEs and nonlinear Sobolev equations arise.…”

Section: Introductionmentioning

confidence: 99%

Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis

Shahzad,

Ahmed,

Baber

et al. 2023

Sci Rep

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In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel techniques used to explore the solitary wave structures namely as; generalized Riccati equation mapping and modified auxiliary equation (MAE) methods. The different types of abundant families of solutions in the form of dark soliton, bright soliton, solitary wave solutions, mixed singular soliton, mixed dark-bright soliton, periodic wave, and mixed periodic solutions. The linearized stability of the model has been investigated. Solitons behave differently in different circumstances, and their behaviour can be better understood by building unique physical problems with particular boundary conditions (BCs) and starting conditions (ICs) based on accurate soliton solutions. So, the choice of unique physical problems from various solutions is also carried out. The 3D, line graphs and corresponding contours are drawn with the help of the Mathematica software that explains the physical behavior of the state variable. This information can help the researchers in their understanding of the physical conditions.

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Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions

Cited by 44 publications

References 32 publications

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

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

Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis

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