Binary Bell polynomials, Hirota bilinear approach to Levi equation

Tang, Yaning; Zai, Weijian; Tao, Siqiao; Guan, Qing

doi:10.1016/j.amc.2016.08.022

Cited by 4 publications

(1 citation statement)

References 28 publications

(27 reference statements)

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“…By using the Wronskian technique, the double Wronskian solution of the non-isospectral Levi equations is derived in [56]. In [58], by the binary Bell polynomial and Hirota method, the bilinear Bäcklund transformations, Lax pair, Darboux transformation as well as the infinite conservation laws of equation (1) are studied. In this research, we are going to give general high-order lump solutions for equation (1) based on the Hirota bilinear method and KP hierarchical method.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

Zhang¹,

Tang²,

Zhang³

et al. 2023

Phys. Scr.

Self Cite

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Exact solutions of magnetohydrodynamic flow of PTT fluid

Faraz

Hou

et al. 2018

J. Phys.: Conf. Ser.

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Solitons, Breathers, and Lump Solutions to the (2 + 1)‐Dimensional Generalized Calogero–Bogoyavlenskii–Schiff Equation

Cheng

Deng

2021

Complexity

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In this paper, a generalized (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff equation is considered. Based on the Hirota bilinear method, three kinds of exact solutions, soliton solution, breather solutions, and lump solutions, are obtained. Breathers can be obtained by choosing suitable parameters on the 2-soliton solution, and lump solutions are constructed via the long wave limit method. Figures are given out to reveal the dynamic characteristics on the presented solutions. Results obtained in this work may be conducive to understanding the propagation of localized waves.

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Binary Bell polynomials, Hirota bilinear approach to Levi equation

Cited by 4 publications

References 28 publications

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

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

Exact solutions of magnetohydrodynamic flow of PTT fluid

Solitons, Breathers, and Lump Solutions to the (2 + 1)‐Dimensional Generalized Calogero–Bogoyavlenskii–Schiff Equation

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