Novel Soliton Interaction Behaviours in the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System

Dai, Chao-Qing; Zhang, Wenting; Chen, Wei-Lu

doi:10.1016/s0034-4877(13)60029-4

Cited by 9 publications

(6 citation statements)

References 21 publications

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“…There exist solitary wave solutions, uncountably infinite smooth and nonsmooth periodic wave solutions [23]. The results in [24] demonstrated fully elastic interactions among special dromion-pair, dromion-pair peakon and dromion-pair semifoldon. The requirements to ensure the analyticity, positiveness and localization of lump solutions were discussed [25].…”

Section: Introductionmentioning

confidence: 90%

Resonant collisions among diverse solitary waves of the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation

J¹,

Li²,

Li³

2022

Phys. Scr.

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According to N-soliton solutions generated by the Hirota’s bilinear method, the resonant collisions among diverse solitary waves can be obtained when the phase shifts of involved solitary waves tend to infinity. Under this constraint, the resonant collisions among a lump and dark line solitons can be derived from that of a breather and dark line solitons by means of an ingenious limiting approach. This paper takes the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation as an example to introduce how to utilize this constraint to derive the resonant collisions among different solitary waves containing breather, lump and dark line solitons in detail. At the same time, the dynamic behaviors of the interacting waveforms are exhibited visually by some figures which include intriguing phenomena. And the characteristics and properties of these interacting waveforms are discussed analytically. In terms of feasibility and practicability, the procedures of analysis in this paper can be exploited widely to study resonant collisions of different waveforms in other integrable systems. The results obtained would enhance the completeness of nonlinear localized wave theory.

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Section: Introductionmentioning

confidence: 90%

Resonant collisions among diverse solitary waves of the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation

J¹,

Li²,

Li³

2022

Phys. Scr.

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“…This hot potato is firstly handled by Zhang and Xu in [7]. Then, it is extended to an (1+1)-dimensional long-wave-short-wave resonant interaction equation [8], Boiti system [9], KdV equation [10,11], asymmetric NNV equation [12], Broer-Kaup system [13,14] and breaking soliton equation [15]. Using the MLVSA results, Lou [16,17,18] finds a common expression…”

Section: Introductionmentioning

confidence: 99%

Direct separation approach and multi-valued localized excitation for (M+N)-dimensional nonlinear system

Xie

2023

Chinese Journal of Physics

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Section: Introductionmentioning

confidence: 99%

Direct separation approach and multi-valued localized excitation for (M+N)-dimensional nonlinear system

Li¹,

Wang

Zhu³

et al. 2022

Preprint

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In this paper, we propose a new variable separation method which does not need Hirota’s bilinear form and directly gives analytic form of solution u instead of its potential uy. This new method not only covers N-soliton solution obtained by Hirota’s direct method but also multi-valued solution of multi-linear variable separation approach(MLVSA), and applicable to (M+N)-dimensional nonlinear model. We would like to call it “direct separation approach” (DSA). Taking the extended (3+1)-dimensional KP equation as an example, we first construct two types of N-soliton solution. Then, by introducing multi-valued functions, rogue wave and four typical folded solitary waves are obtained. In addition, we study the head-on and chase-after collision between two, three, four folded solitary waves, and systematically analyze their dynamic behaviors. Many novel structures are obtained that may help simulate complex folded appearance in real life.

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Novel Soliton Interaction Behaviours in the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System

Cited by 9 publications

References 21 publications

Resonant collisions among diverse solitary waves of the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation

Resonant collisions among diverse solitary waves of the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation

Direct separation approach and multi-valued localized excitation for (M+N)-dimensional nonlinear system

Direct separation approach and multi-valued localized excitation for (M+N)-dimensional nonlinear system

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