Multiple breathers and rational solutions to Ito integro-differential equation arising in shallow water waves

Batool, Tahira; Rizvi, Syed T. R.; Seadawy, Aly R.

doi:10.1016/j.geomphys.2022.104540

Cited by 16 publications

(4 citation statements)

References 41 publications

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“…A partial differential equation (PDE) depicts the relationships between several partial derivatives of a variety of multivariate functions. Physics and engineering are two mathematics-based sciences that frequently use PDEs [1][2][3][4]. The fundamentals of contemporary scientific logic are formed by them for several ideas, including heat, sound, diffusion, electrodynamics [5][6][7], electrostatics, elastic, hydrodynamics, and quantum mechanics [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

2023

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We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solutions, rational kink cross-solutions (RKCs), and homoclinic breather solutions (HBs), and by using the appropriate values for the relevant parameters, their dynamics are visualized in figures. Additionally, two different types of interactions between MSRs and kink waves are analyzed. Furthermore, we examine the stability of the obtained solutions and create a corresponding table. We analyze the stability of these solutions and the movement role of the wave by making graphs as two-dimensional, three-dimensional and density graphs as well as contour visual and stream plots.

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Section: Introductionmentioning

confidence: 99%

“…Zayed et al investigated a two-variable ( G G , 1 G ) expansion technique for the nonlinear KdV equation [45]. By using the symbolic computation with various ansatz transformations for Equation (1), this manuscript aims to evaluate MSR and their interactions with one and two kink waves, PCRs, RKCs, multi-wave solutions, and HBs.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

2023

Self Cite

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“…Nonlinear evolution equations (NLEEs) are significantly used to observe numerous physical phenomena that appear in mathematical physics, condensed matter physics, water surface gravity waves, ion-acoustic waves in plasmas etc. [7,9,27,29,30,36]. The exact solutions for NLEEs play a vital role to study the dynamics of the evolution of native phenomena.…”

Section: Introductionmentioning

confidence: 99%

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields

Batool

Seadawy

Rizvi

2023

NAMC

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In this article, lump solutions, lump with I-kink, lump with II- kink, periodic, multiwaves, rogue waves and several other interactions such as lump interaction with II-kink, interaction between lump, lump with I-kink and periodic, interaction between lump, lump with II-kink and periodic are derived for Pavlov equation by using appropriate transformations. Additionally, we also present 3-dimensional, 2-dimensional and contour graphs for our solutions.

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“…By the direct function approach and matrix form function, Hu and his collaborators derived the hyperbolic function wave, cosine function wave solutions and their mixed solutions [21,22]. In [23], the authors obtained multiple breather solitons and rational solutions by the ansatz function method. Despite all this progress, there are still many important questions on solitons to do.…”

Section: Introductionmentioning

confidence: 99%

Degenerate behaviors and decompositions of the two-soliton solution in the (1+1)-dimensional Ito equation

Wang,

et al. 2023

Phys. Scr.

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In this paper, we investigate the degenerate behaviors and decompositions of two-soliton solution on the non-vanishing constant background for the (1+1)-dimensional Ito equation. By tuning the background constant, interaction phenomena of various types such as the elastic interaction of solitons, fission or fusion phenomena are presented. The degenerate two-soliton solutions which lead to a higher amplitude soliton in collisions of two solitons or describe the decay of a soliton into two new solitons are obtained. To better understand the nature of these interaction phenomena, we explore different decompositions to express the two-soliton solution as a sum of two functions. One of the function exhibits a special soliton excited by the collisions of two solitons, and the other describes the energy exchange of two solitons. Finally, under the module resonance of wave numbers, other types of the degenerate solutions of two solitons are derived and analyzed, such as the breather and rogue wave solutions.

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Multiple breathers and rational solutions to Ito integro-differential equation arising in shallow water waves

Cited by 16 publications

References 41 publications

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields

Degenerate behaviors and decompositions of the two-soliton solution in the (1+1)-dimensional Ito equation

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