Lump solutions to an integrable (3 + 1)-dimensional Boussinesq equation and its dimensionally reduced equations in shallow water

Yao, Shao-Wen; Nuruzzaman, Md.; Kumar, Dipankar; Tamanna, N.K.; İnç, Mustafa

doi:10.1016/j.rinp.2023.106226

Cited by 9 publications

(4 citation statements)

References 33 publications

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“…This section discuss on recent findings in conjunction with a comparison of previous study 38 where the authors investigated the integrable (3+1)-dimensional Boussinesq model to obtain lump solutions. In our work, we proposed the unified Riccati equation expansion method for (3+1)-dimensional Boussinesq model and minimized their dimensional models in shallow water waves to find dark, unique, periodic, and rational solutions.…”

Section: Resultsmentioning

confidence: 85%

“…Now comprehend the dynamics of wave propagations on the ocean surfaces, our goal is to construct the exact solutions to a novel integrable (3+1)-dimensional Boussinesq model by implementing the unified Riccati equation expansion technique 37 . We take into consideration the innovative (3+1)-dimensional Boussinesq model 38 to accomplish these goals. where and are constants and ( x , y , z ) and t shows the spatial and temporal parameters, respectively.…”

Section: Introductionmentioning

confidence: 99%

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The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Nadeem,

Islam,

Şenol

et al. 2024

Sci Rep

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In this study, we examine multiple perspectives on soliton solutions to the (3+1)-dimensional Boussinesq model by applying the unified Riccati equation expansion (UREE) approach. The Boussinesq model examines wave propagation in shallow water, which is derived from the fluid dynamics of a dynamical system. The UREE approach allows us to derive a range of distinct solutions, such as single, periodic, dark, and rational wave solutions. Furthermore, we present the bifurcation, chaotic, and sensitivity analysis of the proposed model. We use planar dynamical system theory to analyze the structure and characteristics of the system’s phase portraits. The current study depends on a dynamic structure that has novel and unexplored results for this model. In addition, we display the behaviors of associated physical models in 3-dimensional, density, and 2-dimensional graphical structures. Our findings demonstrate that the UREE technique is a valuable mathematical tool in engineering and applied mathematics for studying wave propagation in nonlinear evolution equations.

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Section: Resultsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Nadeem,

Islam,

Şenol

et al. 2024

Sci Rep

View full text Add to dashboard Cite

show abstract

“…The authors focus on the study of the breather waves, periodic cross-lump waves and complexiton type solutions for the (2+1)-dimensional Kadomtsev-Petviashvili equation [21]. Yao et al investigated lump solutions for a new integrable (3+1)dimensional Boussinesq equation by using the Hirota bilinear method [22]. Guo et al got the Nth-order rogue wave solutions by constructing a generalized Darboux transformation for the nonlinear Schrödinger equation [23].…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions and the interaction behaviour of the (3+1)-dimensional Jimbo-Miwa-like equation

Ma,

Qi,

Deng

2024

Phys. Scr.

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In this article, we aim to study the dynamical behavior of the (3+1)-dimensional Jimbo- Miwa-like (JML) equation. By using different methods, different forms of solutions are ob- tained. At the same time, in the same method, we also study the influence of parameters on the solution by changing the values of parameters. Firstly, we use the bilinear method to obtain the Y -type and X-type soliton solutions. Secondly, using different test functions, we obtain the interaction phenomenon between the solutions, which is obtained by a lump so- lution and a kink wave solution or by a lump solution and multi-kink wave solutions. Lastly, on the basis of the study of the single lump solution, we have made a further exploration. We not only obtain the lump-periodic solution, which verifies the periodicity, but also obtain the lump-soliton solution. For the above wave solutions, we graphically describe their dynamical properties with MAPLE. It is worth mentioning that the content of our study is different from the existing research: we not only use different methods to study the solutions of the JML equation, but also use different parameter relations and different values of parameters to study the changes of solutions. At the same time, we also use different test functions to study the same form of wave solutions. It is intuitive to see the influence of the test func- tion on the dynamic behavior of the solution. In addition, our results not only enable us to understand the dynamic properties of such equations more intuitively, but also provide some ideas for researchers to facilitate more indepth exploration.

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“…The Darboux transformations was used to study the Ablowitz-Kaup-Newell-Segur (AKNS) equations [4] and the NLS equation [5]. The Hirota bilinear method has been a powerful tool in constructing soliton solutions for several equations, including the Kadomtsev-Petviashvili (KP) equation [6], Sawada-Kotera-Kadomtsev-Petviashvili equation [7] and the (3+1)-dimensional Boussinesq equation [8]. The Riemann-Hilbert approach was employed in the study of multicomponent AKNS integrable hierarchies [9] and the short pulse equation [10].…”

Section: Introductionmentioning

confidence: 99%

Integrability and exact solutions of the (2+1)-dimensional variable coefficient Ito equation

Chu,

Liu,

Chen

2023

Nonlinear Dyn

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This paper focuses on the study of the (2+1)-dimensional Ito equation with spatially variable coefficients. The Lax integrability of the equation is confirmed by the Lax pair derived from the Bell polynomials. In addition, the Hirota bilinear form, the Bäcklund transformation and infinite conservation laws of the equation are obtained by the Bell polynomials. More importantly, the ansatz method and the Hirota bilinear method are employed to construct different types of N-soliton solutions and interaction solutions for the (2+1)-dimensional Ito equation with different coefficient functions. All these solutions are presented graphically.

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Lump solutions to an integrable (3 + 1)-dimensional Boussinesq equation and its dimensionally reduced equations in shallow water

Cited by 9 publications

References 33 publications

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Soliton solutions and the interaction behaviour of the (3+1)-dimensional Jimbo-Miwa-like equation

Integrability and exact solutions of the (2+1)-dimensional variable coefficient Ito equation

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