Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach

Fahim, Md. Rezwan Ahamed; Kundu, Purobi Rani; Islam, Md. Ekramul; Akbar, M. Ali; Osman, M. S.

doi:10.1016/j.joes.2021.08.009

Cited by 96 publications

(19 citation statements)

References 43 publications

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“…In recent years, the research on the exact solution and integrability of NLEEs have been developed rapidly [4,5], which is of great significance to understand the nonlinear mechanism. In the past decades, many effective methods have been developed to find the exact solution to NLEEs, such as the Hirota bilinear method [6,7], Bäcklund transformation (BT) [8,9], Bell polynomial [4,5], long wave limit method [10,11], Lie symmetry analysis [12,13], and the sine-Gordon expansion approach [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation

2023

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The (1+1)-dimensional bilinear Hietarinta equation was firstlyproposed when searching for integrable nonlinear evolution equationsby the three-soliton method. In this paper, we focus on the(2+1)-dimensional extension of Hietarinta equation, which enjoyspotential application in environmental engineering. Based on thebilinear form, one-soliotn and two-soliton solutions are derived. Asan aspect of integrability, bilinear B"acklund transformation andBell-polynomial-typed B"acklund transformation are derived throughthe Hirota bilinear method and Bell polynomials, respectively. Thethree-dimensional plots of soliton solutions have been given byselecting appropriate parameters.

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Section: Introductionmentioning

confidence: 99%

Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation

2023

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“…The study of the soliton solutions can provide a theoretical reference for the research of nonlinear physical models, soliton control, optical switching equipment, and so on. Up to now, many effective and powerful methods have been obtained for constructing the soliton solutions of the NLPDEs: the extended trial equation method [1,2], generalized exponential rational function method [3], sine-Gordon expansion method [4][5][6], generalized (G′/G) expansion method [7], extended rational sinecosine and sinh-cosh method [8,9], F-expansion method [10][11][12], Cole-Hopf transformation [13,14], exp-function method [15][16][17], extended tanh-function method [18][19][20], Bäcklund transformation [21], Sardar subequation method [22,23], and so on [24][25][26][27][28][29][30][31]. In this paper, we aim to study the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation (HFSCE) that is given by [32]:…”

Section: Introductionmentioning

confidence: 99%

Abundant Soliton Structures to the ( $2 + 1$ )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model

Wang

Shi

Wang

2023

Advances in Mathematical Physics

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In this paper, we aim to investigate the ( 2 + 1 )-dimensional Heisenberg ferromagnetic spin chain equation that is used to describe the nonlinear dynamics of magnets. Two recent effective technologies, namely, the variational method and subequation method, are employed to construct the abundant soliton solutions. By these two methods, diverse solutions such as the bright soliton, dark soliton, bright-dark soliton, perfect periodic soliton, and singular periodic soliton are successfully extracted. The numerical results are illustrated in the form of 3-D plots and 2-D curves by choosing proper parametric values to interpret the dynamics of wave profiles. Finally, the physical interpretation of the acquired results is elaborated in detail. The results obtained in this study are helpful to explain some physical meanings of some nonlinear physical models in electromagnetic waves.

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“…Before Russell's work was proven in the 1870s, prominent philosophers and scientists widely praised its scientific implications. Nonetheless, Rayleigh and Boussinesq's work demonstrates the critical issue of non-linearity and dispersion, It is still rendering to address Stokes and Airy's argument against using kink-shaped and bell-shaped solutions to simulate wave phenomena in the optical fibre, the elastic media and other important fields, well-known examples include the travelling wave solutions of Korteweg de Vries and the Boussinesq equation [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

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In this article, the new extended direct algebraic method is used to build the exact travellingwave solutions for the non-linear time-fractional Clannish Random Walker’s Parabolic equation.This study establishes the framework in which periodic, singular, dark, bright and kink-typewave solitons are obtained with exact solutions offered by the mixed hyperbolic and trigonom-etry solutions, mixed periodic and periodic solutions, plane solutions, shock solutions, mixedtrigonometric solutions, mixed singular solutions, mixed shock single solutions, complex solitarysingular solutions, shock solutions and shock wave solutions. The exact soliton solutions of thetime-fractional clannish random walker’s parabolic equation model is graphically presented atdifferent values of involved parameters by Wolfram Mathematica software. The propagating behaviours display in 3-D, contour and 2-D surfaces of the obtained results to visualise the im-pact of the involved parameters. The sensitivity analysis is demonstrated for the wave profilesof the designed dynamical framed structure, where the soliton wave number parameter regulatesthe water wave singularity. This analysis illustrates that the utilized method is efficient andreliable and can be useful to find appropriate solutions in closed-form solitary soliton to a wide range of non-linear evolution equations. These techniques can also be utilised to find new exact travelling wave solutions for any class of integer or fractional differential equations thatarise in mathematical physics.

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Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach

Cited by 96 publications

References 43 publications

Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation

Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation

Abundant Soliton Structures to the ( $2 + 1$ )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

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Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach

Cited by 96 publications

References 43 publications

Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation

Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation

Abundant Soliton Structures to the ( 2 + 1 )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

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Abundant Soliton Structures to the ( $2 + 1$ )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model