General high-order rational solutions and their dynamics in the (3+1)-dimensional Jimbo–Miwa equation

Tang, Yaning; Zhang, Qing; Zhou, Bingchang; Wang, Yan; Zhang, Yetong

doi:10.1007/s11071-022-07560-x

Cited by 3 publications

(1 citation statement)

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“…When a b , For the NLS equation, it has been shown graphically by Ohta and Yang [54] that when one of the internal parameters in the rogue wave solutions is large enough, its third-order rogue waves may be comprised of six individual first-order rogue waves, and they form triangle or pentagon. Surprisingly, these patterns also appear in the third-order rogue wave solutions of many other integrable systems [60]. We show that the Levi equations share analogous features(see figures 3(c) and 4(c)).…”

Section: High-order Lump Solutions (N > 1)supporting

confidence: 59%

General high-order lump solutions and their dynamics in the Levi equations

Zhang¹,

Tang²,

Zhang³

et al. 2023

Phys. Scr.

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General high-order lump solutions are derived for the Levi equations based on the Hirota bilinear method and Kadomtsev–Petviashvili (KP) hierarchy reduction technique. These lump solutions are given in terms of Gram determinants whose matrix elements are connected to Schur polynomials. Thus, our solutions have explicit algebraic expressions. Their dynamic behaviors are analyzed by using density maps. It is shown that when the absolute value of one group of these internal parameters in the lump solutions is very large, lump solutions exhibit obvious geometric structures. Interestingly, we have shown that their initial and middle state solutions possess various exciting geometric patterns, including hexagon, decagon, tetradecagon, etc. and other quasi-structures in addition to the standard triangle, pentagon type patterns. Because the internal parameters are not complex conjugates of each other, the dynamic behaviors of solutions are richer. These results make several contributions to the current literature and have a number of important implications for further analysis of fluid dynamics in non-homogeneous media.

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Section: High-order Lump Solutions (N > 1)supporting

confidence: 59%