Interactions between soliton and rogue wave for a (2+1)-dimensional generalized breaking soliton system: Hidden rogue wave and hidden soliton

Ma, Yu‐Lan; Li, Bang‐Qing

doi:10.1016/j.camwa.2019.03.002

Cited by 76 publications

(17 citation statements)

References 74 publications

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“…The soliton molecule and lump wave of ( 20) are worthy of study by the velocity resonance mechanism and the symbolic computation approach. Rogue waves are unexpectedly high-amplitude single waves that have been reported by using the Hirota bilinear method [50,51]. These nonlinear excitations of (20) are valuable to increase understanding of the phenomena between different nonlinear waves.…”

Section: Resultsmentioning

confidence: 99%

Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation

Ren

2021

Advances in Mathematical Physics

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The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2 + 1 -dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2 + 1 -dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual 2 + 1 -dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all directions and decays algebraically. The lump solution of the higher-order Boussinesq equation is obtained by using a quadratic function. This lump wave is just the bright form by some detail analysis. The graphics in this study are carried out by selecting appropriate parameters. The results in this work may enrich the variety of the dynamics of the high-dimensional nonlinear wave field.

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Section: Resultsmentioning

confidence: 99%

Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation

Ren

2021

Advances in Mathematical Physics

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“…Although the integrable system studied in this paper is not the same system as those in Refs. [55,56], they have similar fusion and fission phenomena.…”

Section: The Mixed Solution Composed Of One Rational Lump and One Linmentioning

confidence: 96%

“…In the interaction processes between one lump and one line solitary wave, fission and fusion phenomena [55,56] will appear under the different parameters. If we set x and y as constants, the structure of the mixed solution equation (16) can be explained as follows.…”

Section: The Mixed Solution Composed Of One Rational Lump and One Linmentioning

confidence: 99%

Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

Yao

Xie

Hui

2021

Advances in Mathematical Physics

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Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution describes the interaction between one lump and one line solitary wave, which exhibits fission and fusion phenomena under the different parameters. The other kind of the mixed solution shows one lump interacting with two paralleled line solitary waves, in which the evolution of the lump gives rise to a two-dimensional rogue wave. This shows that these three interesting phenomena exist in the corresponding physical model.

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“…Interaction solutions occur between lump solutions and one stripe [23,24,25,26,27,28] or line soliton based on Hirota bilinear form and combining the rational quadratic functions (exponential functions) were analyzed in [29,30], such as (4 + 1)-dimensional Fokas and (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation [31].…”

Section: Introductionmentioning

confidence: 99%

Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

Elboree

2020

Math. Model. Nat. Phenom.

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In this paper, we consider the (3 + 1)-dimensional Burgers-like equation which arises in fluid mechanics, which constructed from Lax pair generating technique. The bilinear form for this model is obtained to construct the multiple-kink solutions. Lump solution, rogue wave solutions are constructed via the obtained bilinear form for this model. The physical phenomena for these solution are analyzed by studying the influence of the parameters for these solutions. The phase shifts, propagation directions and amplitudes for these solutions are controlled via these parameters. .The collisions between the lump wave and the stripe soliton, which is called lumpo solution are completely nonelastic interaction. Finally, the figures of the solutions are shown to study the dynamical behavior for the lump, rogue wave and the properties of the interaction phenomena under various parameters for (3 + 1)-dimensional Burgers-like equation. These results can't be found in the previous scientific papers.

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Interactions between soliton and rogue wave for a (2+1)-dimensional generalized breaking soliton system: Hidden rogue wave and hidden soliton

Cited by 76 publications

References 74 publications

Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation

Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation

Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

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Interactions between soliton and rogue wave for a (2+1)-dimensional generalized breaking soliton system: Hidden rogue wave and hidden soliton

Cited by 76 publications

References 74 publications

Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation

Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation

Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

Contact Info

Product

Resources

About

Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation

Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation