Lump solutions, Kuznetsov–Ma breathers, rogue waves and interaction solutions for magneto electro-elastic circular rod

Seadawy, Aly R.; Rizvi, Syed T. R.; Ahmed, Sarfaraz; Bashir, Azhar

doi:10.1016/j.chaos.2022.112563

Cited by 28 publications

(6 citation statements)

References 34 publications

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“…Painlevé analysis has been used to determine whether the NLEEs are Painlevé integrable or not [12][13][14]. Researchers have committed to the analytic solutions for the NLEEs, including the lump, soliton and rogue wave solutions [15][16][17][18][19][20][21]. The lump solutions have been found to be the rational-polynomial ones that are local in all directions of the space [22].…”

Section: Introductionmentioning

confidence: 99%

“…The lump solutions have been found to be the rational-polynomial ones that are local in all directions of the space [22]. It has been seen that the lump solutions can be obtained directly or via the long wave limit of the soliton solutions [13,16]. Rogue waves, appearing from nowhere and disappearing without a trace, have been known as the nonlinear waves localized in both time and space [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Painlevé analysis and inelastic interactions of the lumps for a generalized (2+1)-dimensional Korteweg-de Vries system for the shallow-water waves

Liu,

Tian,

Gao

2024

Phys. Scr.

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Water waves, one of the common natural phenomena, are recognized as complexand often turbulent. A generalized (2+1)-dimensional Korteweg-de Vries system forthe shallow-water waves is conducted in this paper. We perform the Painlev´e analysisand find that the system is Painlev´e integrable. We study the inelastic interactions ofthe lumps for the system. We find that two lumps, which propagate along the curveswith the equal amplitude, are symmetric about the x axis before the interaction, wherex is a scaled spatial variable. After the interaction, amplitudes of the two lumps aredifferent, but in the process of moving, the lower lump gradually increases, while thehigher lump gradually decreases, and the velocities of two lumps at the infinity areequal. We observe two different inelastic interactions of the three lumps: (1) thethree lumps are symmetric in time and space, and they slowly contract (before theinteraction) and swell (after the interaction); (2) the three lumps slowly fuse and afterthe interaction they form a straight line forward, and their amplitudes are graduallyequal when t → ∞.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Painlevé analysis and inelastic interactions of the lumps for a generalized (2+1)-dimensional Korteweg-de Vries system for the shallow-water waves

Liu,

Tian,

Gao

2024

Phys. Scr.

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“…A soliton is a wave that retains its shape and velocity on collision with another soliton. Many researchers have worked on finding the soliton solutions of the models [34][35][36][37][38][39][40] by different techniques.…”

Section: Introductionmentioning

confidence: 99%

Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

Ali,

Seadawy,

Rizvi

et al. 2024

Commun. Theor. Phys.

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In this article, we explore the famous Selkov-Schnakenberg (SS) system of coupled nonlinear partial differential equations (PDEs) for Lie symmetry analysis (LSA), Self Adjointness (SA) and Conservation laws (CLs). Moreover miscellaneous soliton solutions like dark, bright, periodic, rational, Jacobian elliptic function (JEF), Weierstrass elliptic and hyperbolic solutions of SS system will be achieved by a well-known technique called Sub-ODE. All these results are displayed graphically by 3D, 2D and contour plots.

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“…Rogue waves [27][28][29][30][31][32][33], sometimes known as enormous solitary waves that 'come from nowhere' in the water, are localized in space-time with significant amplitude. They can severely harm people since they are unexpected and extensive.…”

Section: Introductionmentioning

confidence: 99%

Newly formed center-controlled rouge wave and lump solutions of a generalized (3+1)-dimensional KdV-BBM equation via symbolic computation approach

2023

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In this article, we investigate the generalized (3+1)-dimensional KdV-Benjamin-Bona-Mahony equation governed with constant coefficients. It applies the Painlev'e analysis to test the complete integrability of the concerned KdV-BBM equation. The symbolic computational approach provides first-order, second-order rogue wave and lump solutions with center-controlled parameters. The rogue waves localized in space and time have a significant amplitude, and lumps are of rational form solution, localized decaying solutions in all space directions rationally. Utilizing a symbolic computation approach, we get the bilinear equation of the KdV-Benjamin-Bona-Mahony equation and show the center-controlled rogue waves and lumps. We employ the symbolic system software \textit{Mathematica} to do the symbolic computations, form the first and second-order rogue waves, and lump solutions with appropriate values of constant coefficients. The KdV-Benjamin-Bona-Mahony equation analyses the evolution of long waves with modest amplitudes propagating in plasma physics and the motion of waves in fluids and other weakly dispersive mediums. Moreover, rogue waves and lumps occur in several scientific areas, such as fluid dynamics, optical fibers, dusty plasma, oceanography, water engineering, and other nonlinear sciences.

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Lump solutions, Kuznetsov–Ma breathers, rogue waves and interaction solutions for magneto electro-elastic circular rod

Cited by 28 publications

References 34 publications

Painlevé analysis and inelastic interactions of the lumps for a generalized (2+1)-dimensional Korteweg-de Vries system for the shallow-water waves

Painlevé analysis and inelastic interactions of the lumps for a generalized (2+1)-dimensional Korteweg-de Vries system for the shallow-water waves

Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

Newly formed center-controlled rouge wave and lump solutions of a generalized (3+1)-dimensional KdV-BBM equation via symbolic computation approach

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