Rogue heat and diffusion waves

Bayındır, Cihan

doi:10.1016/j.chaos.2020.110047

Cited by 3 publications

(1 citation statement)

References 29 publications

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“…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]. A resonant solution has been obtained when a phase shift caused by the interaction between the solitons/breathers becomes infinite [25].…”

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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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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