Characteristics of the Lumps and Stripe Solitons with Interaction Phenomena in the (2 + 1)-Dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada Equation

Deng, Zhi-Hao; Xu, Chunju; Tan, Jia-Ning; Tang, Bing; Deng, Ke

doi:10.1007/s10773-018-3912-2

Cited by 14 publications

(8 citation statements)

References 51 publications

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“…We introduce the similarity transformations u(x, y, z, t) = U (z, t), z = α(t) x + β(t) y, and t := t;thus, (7) is rewritten as…”

Section: Outlines Of the Eummentioning

confidence: 99%

“…We consider the case when p = 1. By inserting ( 9) into (7), we find that the balance condition gives rise to n = k − 1. For the consistency condition, we need to calculate:…”

Section: Polynomial Solutionsmentioning

confidence: 99%

“…By means of the HBM, lump-type solution and two types of interaction solutions of the 2D-Caudrey-Dodd-Gibbon-Kotera-Sawada equation were obtained [6]. The interaction phenomenon between the lump waves and stripe solitons in the 2D-CDGKSE, by making use of the HBM, was investigated [7]. The CDGKS hierarchy associated with a matrix spectral problem was suggested, based on Lenard recursion equations [8].…”

Section: Introductionmentioning

confidence: 99%

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Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

Abdel‐Gawad

2022

Nonlinear Dyn

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A Generalized (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation (2D- gCDGKSE) is an integro-differential equation that describes tow-layer fluid interaction. The non-autonomous (2+1)-dimensional gCDGKSE (NAUT-gCDGKSE) was rarely considered in the literature. In the previous works, the concepts of two-layer fluid interaction and non-uniform fluid were not explored. This motivated us to focus the attention on these themes. Our objective is to inspecting waves structures in non-uniform fluid which describes fluid flows near a solid boundary. Thus, the present work is completely new. Our objective, here, is to inspect waves which are similar to those created in waterfall, water waves behind dams, boat sailing, in the network of canals during water release, and internal waves in submarine. In a uniform fluid, rogue waves occur in open oceans and seas, while in the present case of non-uniform fluid, towering and internal rogue waves occur near barriers (islands) and near submarine, respectively. This was consolidated experimentally, as it was shown that rogue wave is produced in a water tank (which is with solid boundary). The exact solutions of NAUT-gCDGKSE are derived here, by implementing the extended unified method (EUM). In applications, it is found that the EUM is of lower time cost in symbolic computation, than when using Lie symmetry, Darboux and AutoBucklund transformations. The results obtained here are evaluated numerically, and they are displayed in graphs. They reveal multiple waves structures with relevance to waves created near a solid boundary. Among them are towering and internal rogue waves, internal (hollowed) and bulge-U-shape wave and S-shape wave, water fall, saddle wave, and dromoions.

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“…We introduce the similarity transformations u(x, y, z, t) = U (z, t), z = α(t) x + β(t) y, and t := t;thus, (7) is rewritten as…”

Section: Outlines Of the Eummentioning

confidence: 99%

“…We consider the case when p = 1. By inserting ( 9) into (7), we find that the balance condition gives rise to n = k − 1. For the consistency condition, we need to calculate:…”

Section: Polynomial Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

Abdel‐Gawad

2022

Nonlinear Dyn

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“…The (2+1)-dimensional Sawada-Kotera equation [24][25][26], the Bogoyavlensky-Konoplechenko equation [27][28][29], the Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation [30][31][32] are special cases of (3). Many scholars have studied (2+1)-dimensional gKDKK equation from different angles.…”

Section: Introductionmentioning

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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“…e paper is organized as follows. In Section 2, the nonautonomous lump solutions of equation 2will be derived based on Hirota's bilinear form [39][40][41][42]. In Section 3, the accelerated and decelerated motions of lump waves will be investigated analytically.…”

Section: Introductionmentioning

confidence: 99%

Nonautonomous Motion Study on Accelerated and Decelerated Lump Waves for a (3 + 1)‐Dimensional Generalized Shallow Water Wave Equation with Variable Coefficients

et al. 2019

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Under investigation in this paper is a (3 + 1)-dimensional variable-coefficient generalized shallow water wave equation. The exact lump solutions of this equation are presented by virtue of its bilinear form and symbolic computation. Compared with the solutions of the previous cases, these solutions contain two inhomogeneous coefficients, which can show some interesting nonautonomous characteristics. Three types of dispersion coefficients are considered, including the periodic, exponential, and linear modulations. The corresponding nonautonomous lump waves have different characteristics of trajectories and velocities. The periodic fission and fusion interaction between a lump wave and a kink soliton is discussed graphically.

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Characteristics of the Lumps and Stripe Solitons with Interaction Phenomena in the (2 + 1)-Dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada Equation

Cited by 14 publications

References 51 publications

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

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

Nonautonomous Motion Study on Accelerated and Decelerated Lump Waves for a (3 + 1)‐Dimensional Generalized Shallow Water Wave Equation with Variable Coefficients

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