A new (3+1)-dimensional Sakovich equation in nonlinear wave motion: Painlevé integrability, multiple solitons and soliton molecules

Ma, Yu‐Lan; Wazwaz, Abdul‐Majid; Li, Bang‐Qing

doi:10.1007/s12346-022-00689-5

Cited by 30 publications

(9 citation statements)

References 53 publications

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“…Te fndings demonstrate the efcacy as well as the potential of the strategies that were employed. In conclusion, the solutions that we have shown in this work are fully compatible with the analytical solutions that were acquired in the previous work [18]. We have high hopes that this work will be extended to include fractional derivatives in subsequent work, and that we will also be able to solve this equation using a variety of numerical approaches.…”

Section: Discussionsupporting

confidence: 82%

“…Step 3: we attain two families of solutions of (18). Family 1: when ∆ � λ 2 − 4μ > 0 Te solution of ( 17) is as follows: (19) p 1 and p 2 are arbitrary constants, hold the relation…”

Section: 2mentioning

confidence: 99%

“…Newly, Wazwaz et al [18] present an extension to (2) by adding two terms, the frst one is a linear term u zz which characterizes the dispersion efect of the second order along the direction of z-axis and the second term is a nonlinear term uu xx which characterizes the nonlinear efect reasoned by u and the dispersion of the second order along the direction of x-axis, (2) takes the following form:…”

Section: Introductionmentioning

confidence: 99%

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Novel Soliton Solutions for the (3 + 1)-Dimensional Sakovich Equation Using Different Analytical Methods

Ali

AlQahtani

Mehanna³

et al. 2023

Journal of Mathematics

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In the work that we are doing now, our goal is to find a solution to the (3 + 1)-dimensional Sakovich equation, which is an equation that can be used to characterize the movement of nonlinear waves. This approach sees extensive use across the board in engineering’s many subfields. This new equation can represent more dispersion and nonlinear effects, which allows it to accept more different application scenarios. As a result, it has a wider range of potential applications in the physical world. As a consequence of this, when the two components are combined, they can be used to easily counteract the effects of nonlinearity and dispersion on the integrability of partially differential equations. This equation represents a novel physical paradigm that should be looked into further. We use the following three analytical techniques: the exp − ψ η expansion method is the first one, the second is the G ′ / k G ′ + G + r expansion method, and the Bernoulli sub-ODE technique is the last one. Lastly, the soliton solutions obtained are presented by graphs in two and three dimensions, which present different kinds of solitons such as dark, periodic, exponential, bright, and singular soliton solutions.

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Section: Discussionsupporting

confidence: 82%

Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Novel Soliton Solutions for the (3 + 1)-Dimensional Sakovich Equation Using Different Analytical Methods

Ali

AlQahtani

Mehanna³

et al. 2023

Journal of Mathematics

Self Cite

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“…It is worth noting that, some nonlinear equations hold N-soliton molecules, such as, optical transient stimulated Raman scattering equation [37], (3+1)-dimensional Sakovich system [40], (3+1)-dimensional Geng equation [38]. Therefore, proposition 2 is an important observation for the CDG equation (1).…”

Section: The Soliton Moleculesmentioning

confidence: 99%

“…In recent years, soliton molecules, various heterotypic solitons (e.g., solitonʼs fusions and fissions) have been identified as important features according to the soliton resonance view [32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Breather, soliton molecules, soliton fusions and fissions, and lump wave of the Caudrey-Dodd-Gibbon equation

Li,

2023

Phys. Scr.

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In this article, our attention is focused on the exploration of new features of the Caudrey-Dodd-Gibbon (CDG) equation arising from fluid mechanism. We introduce a constant in the transformation, which links the solution and auxiliary function defined in the bilinear form. By constructing different auxiliary function, we calculate the breather solution, one- to three-soliton solutions and lump wave solution. We report that a breather can be generated from a stripe-like soliton. We discover the soliton molecules and their interaction where the maximum amplitude will decrease as they overlap. Two types of heterotypic solitons, namely, soliton fusions and fissions are obtained by attaining their constrain conditions, respectively. We also observe this equation possesses several unique features, such as, having only the two-soliton molecules but not N (N ≥ 3)-soliton molecules, and having the line-like lump wave parallel to the x-axis but not to the t-axis.

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Dynamics of soliton resonances and soliton moleculesfor the AB system in two-layer fluids

2023

Nonlinear Dyn

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A new (3+1)-dimensional Sakovich equation in nonlinear wave motion: Painlevé integrability, multiple solitons and soliton molecules

Cited by 30 publications

References 53 publications

Novel Soliton Solutions for the (3 + 1)-Dimensional Sakovich Equation Using Different Analytical Methods

Novel Soliton Solutions for the (3 + 1)-Dimensional Sakovich Equation Using Different Analytical Methods

Breather, soliton molecules, soliton fusions and fissions, and lump wave of the Caudrey-Dodd-Gibbon equation

Dynamics of soliton resonances and soliton moleculesfor the AB system in two-layer fluids

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