Nonlinear superposition between lump waves and other waves of the (2 $$+$$ 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

Zhao, Zhonglong; He, Lingchao

doi:10.1007/s11071-022-07215-x

Cited by 29 publications

(9 citation statements)

References 47 publications

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“…There are many aspects of (2+1)-dimensional gKDKK equation worth studying. For example, the new constraint proposed in [40,41] can also be applied to this equation. It is hoped that our study can enrich the dynamic behavior of nonlinear evolution equations.…”

Section: Discussionmentioning

confidence: 99%

Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

Gao

Deng

2022

Preprint

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Fission and fusion are common phenomena in nature, they usually occur in physical and biological fields. In this paper, we will give new constraint to obtain fission and fusion solutions which have the shape of the letter Y . In combination with velocity resonance method, mode resonance method and long-wave limit method, we construct the interaction solutions of y-type molecules with soliton molecules, breather molecules and lump molecules respectively. We also obtain a novel solution containing a mixture of lump molecules, breather molecules and y-type molecules. At the same time, we analyze the dynamic behaviors of these interaction solutions and give the problems waiting to be solved.

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Section: Discussionmentioning

confidence: 99%

Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

Gao

Deng

2022

Preprint

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“…Li et al discussed the soliton molecules of the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation and the (2+1)-dimensional fifth-order Korteweg-de Vries(KdV) equation [40,41]. In addition, we studied the nonlinear superposition of the bifurcation of T-resonance Y-type solitons, lumps, breathers, and solitons with the aid of velocity resonance [42,43].…”

Section: Introductionmentioning

confidence: 99%

Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation

et al. 2023

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A (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation is considered systematically. N-soliton solutions are obtained using Hirota’s bilinear method. The employment of the complex conjugate condition of parameters of N-soliton solutions leads to the construction of breather solutions. Then, the lump solution is obtained with the aid of the long-wave limit method. Based on the transformation mechanism of nonlinear waves, a series of nonlinear localized waves can be transformed from breathers, which include the quasi-kink soliton, M-shaped kink soliton, oscillation M-shaped kink soliton, multi-peak kink soliton, and quasi-periodic wave by analyzing the characteristic lines. Furthermore, the molecular state of the transformed two-breather is studied using velocity resonance, which is divided into three aspects, namely the modes of non-, semi-, and full transformation. The analytical method discussed in this paper can be further applied to the investigation of other complex high-dimensional nonlinear integrable systems.

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“…The lump wave is a remarkable localized wave solution degenerating in the whole space. [1][2][3][4][5][6][7] The lump solution is actually a kind of rational solutions from a mathematical point of view, whose simplest form was first discovered by means of the dressing method and the Hirota's bilinear method. [8][9][10] This solution consists of multiple localized peaks remaining their velocities and trajectories unchanged before and after the interactions.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

Zhao¹,

He²,

Wazwaz³

2023

Chinese Phys. B

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A large member of lump chain solutions of the (2+1)-dimensional BKP equation are constructed by means of the τ-function in form of Grammian. The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities. An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains. The degenerate structures of parallel, superimposed and molecular lump chains are presented. The interaction solutions between lump chains and kink-solitons are investigated, where the kink-solitons lie on the boundaries of dominant region determined by the constant term in the τ-function. Furthermore, the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated. The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

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Nonlinear superposition between lump waves and other waves of the (2 $$+$$ 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

Cited by 29 publications

References 47 publications

Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

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