Dynamics of multi-breathers, N-solitons and M-lump solutions in the (2+1)-dimensional KdV equation

Tan, Wenjun; Dai, Zhengde; Yin, Zhaoyang

doi:10.1007/s11071-019-04873-2

Cited by 58 publications

(25 citation statements)

References 31 publications

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“…( 1) with different structural forms are constructed. Under the action of oscillation of breather wave, some lump or lump-type solutions are found out by using parameter limit method [9,21]. Through Painlevé analysis, we assume u(x, y, z, t) = 2(lnf ) x .…”

Section: Evolution and Degeneration From Breather To Lump Solutionmentioning

confidence: 99%

“…proposed to study the M -lump solutions of the integrable systems in [18], this positive method has attracted a lot of researchers' attention. Many valuable and interesting results have sprung up, lump waves of the (2+1)-dimensional nonlinear equations [21][22][23][24][25][26]. Lump solutions of the (3+1)-dimensional nonlinear systems, such as potential Yu-Toda-Sasa-Fukuyama equation [27], Sharma-Tasso-Olver-like equation [28], B-type Kadomtsev-Petviashvili-Boussinesq equation [29,30].…”

Section: Introductionmentioning

confidence: 99%

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Evolution Behaviour of Kink Breathers and Lump-M-Solitons (M → ∞) for the (3+1)-Dimensional Hirota-Satsuma-Ito-Like Equation

Longxing¹

2021

Preprint

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In this paper, some novel lump solutions and interaction phenomenon between lump and kink M-soliton are investigated. Firstly, we study the evolution and degeneration behaviour of kink breather wave solution with difffferent forms for the (3+1)-dimensional Hirota-Satsuma-Ito-like equation by symbolic computation and Hirota bilinear form. In the process of degeneration of breather waves, some novel lump solutions are derived by the limit method. In addition, M-fifissionable soliton and the interaction phenomenon between lump solutions and kink M-solitons (lump-M-solitons) are investigated, the theorem and corollary about the conditions for the existence of the interaction phenomenon are given and proved further. The lump-M-solitons with difffferent types is studied to illustrate the correctness and availability of the given theorem and corollary, such as lump-cos type, lump-cosh-exponential type, lump cosh-cos-cosh type. Several three-dimensional fifigures are drawn to better depict the nonlinear dynamic behaviours including the oscillation of breather wave, the emergence of lump, the evolution behaviour of fission and fusion of lump-M-solitons and so on.

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Section: Evolution and Degeneration From Breather To Lump Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Evolution Behaviour of Kink Breathers and Lump-M-Solitons (M → ∞) for the (3+1)-Dimensional Hirota-Satsuma-Ito-Like Equation

Longxing¹

2021

Preprint

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“…To write above constraint equations into a linear system, we introduce the notations as the formula (16). Then liner system about parameters δ and c can be obtained ( a 11 a 12 a 21 a 22…”

Section: One-periodic Wave Solution and Its Asymptotic Propertiesmentioning

confidence: 99%

“…Lump solution is a rational solution localized in all directions in space, which can be seen limit of the infinite period of the breather wave [10][11][12][13][14]. The long wave limit method is one of the effective methods to construct the multiple lump solutions and the hybrid solutions of the integrable systems that can be transformed into bilinear equations [15][16][17]. The resonant solitary wave is a special kind of soliton.…”

Section: Introductionmentioning

confidence: 99%

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

Zhang

Zhao

2021

Preprint

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In this paper, we consider a generalized (2+1)-dimensional nonlinear wave equation. Based on the bilinear, the N-soliton solutions are obtained. The resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are constructed by adding some new constraints to the parameters of the N-soliton solutions. The new type of two-opening resonance Y-type soliton solutions are presented by choosing some appropriate parameters in 3-soliton solutions. The hybrid solutions consisting of resonance Y-type solitons, breathers and lumps are investigated. The trajectories of the lump waves before and after the collision with the Y-type solitons are analyzed from the perspective of mathematical mechanism. Furthermore, the multi-dimensional Riemann-theta function is employed to investigate the quasi-periodic wave solutions. The one-periodic and two-periodic wave solutions are obtained. The asymptotic properties are systematically analyzed, which establish the relations between the quasi-periodic wave solutions and the soliton solutions. The results may be helpful to provide some effective information to analyze the dynamical behaviors of solitons, fluid mechanics, shallow water waves and optical solitons.

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“…Lump wave is a special kind of rational function wave with the characteristics of energy concentration and localization property in the space [13][14][15][16][17][18]. In the train of the study, a series of methods has been quickly developed to obtain lump wave including the first mathematical description of lump wave [19], the long wave limit method is an effective method proposed to study the M -lump solutions of the integrable systems in [20][21][22][23][24], this positive method has attracted a lot of researchers' attention. the direct method [25][26][27][28][29][30], the parameter limit method [31][32][33][34], complexication method [35,36], bilinear neural network method [37], etc.…”

Section: Introductionmentioning

confidence: 99%

Degeneration of solitons for a ($$3+1$$)-dimensional generalized nonlinear evolution equation for shallow water waves

2022

Nonlinear Dyn

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A the (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves is investigated with different methods. Based on symbolic computation and Hirota bilinear form, Nsoliton solutions are constructed. In the process of degeneration of N -soliton solutions, T -breathers are derived by taking complexication method. Then rogue waves will emerge during the degeneration of breathers by taking the parameter limit method. Through full degeneration of N -soliton, M -lump solutions are derived based on long wave limit approach. In addition, we also find out that the partial degeneration of N -soliton process can generate the hybrid solutions composed of soliton, breather and lump.

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Dynamics of multi-breathers, N-solitons and M-lump solutions in the (2+1)-dimensional KdV equation

Cited by 58 publications

References 31 publications

Evolution Behaviour of Kink Breathers and Lump-M-Solitons (M → ∞) for the (3+1)-Dimensional Hirota-Satsuma-Ito-Like Equation

Evolution Behaviour of Kink Breathers and Lump-M-Solitons (M → ∞) for the (3+1)-Dimensional Hirota-Satsuma-Ito-Like Equation

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

Degeneration of solitons for a ($$3+1$$)-dimensional generalized nonlinear evolution equation for shallow water waves

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