Solitons and periodic waves for the (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Deng, Gao-Fu; Gao, Yi–Tian; Su, Jing-Jing; Ding, Chaoliang; Jia, Ting-Ting

doi:10.1007/s11071-019-05328-4

Cited by 88 publications

(10 citation statements)

References 59 publications

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“…where α and β are two arbitrary constants. For equation ( 1), Deng et al have obtained Nth-order Pfaffian and periodic wave solutions [29], Peng et al have also derived solitary and lump waves and their interaction phenomena [28].…”

Section: Introductionmentioning

confidence: 99%

Resonance Y-shape solitons and mixed solutions for a (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Yue

Deng

2022

Nonlinear Dyn

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Under the well-known bilinear method of Hirota, the specific expression for N-soliton solutions of (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada(gCDGKS) equation in fluid mechanics is given. By defining a noval restrictive condition on N-soliton solutions, resonant Y-type and X-type soliton solutions are generated. Under the previous new constraints, combined with the velocity resonance method and module resonant method, the mixed solutions of resonant Y-type solitons and line waves, breather solutions are found. Finally, with the support of long wave limit method, the interaction between resonant Ytype solitons and higher-order lumps is shown, and the motion trajectory equation before and after the interaction between lumps and resonant Y-type solitons is derived.

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Section: Introductionmentioning

confidence: 99%

Resonance Y-shape solitons and mixed solutions for a (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Yue

Deng

2022

Nonlinear Dyn

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“…In contrast with this, here, these characteristics are dealt with. The solitary wave ansatz method along with HBM and numerical simulations was used to study the CDGKSE and its bidirectional form [29,30]. An algebraic method with symbolic computation was employed to construct a series of exact solutions of the 2D-CDGKSE [31].…”

Section: Introductionmentioning

confidence: 99%

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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“…Fluid dynamics has been seen as the studies of the underlying mechanisms of liquids, gases or plasmas, and the forces on them, and applied to oceanography, astrophysics, meteorology and biomedical engineering [1,2]. Plasma physics has been considered as the studies of charged particles and fluids interacting with self-consistent electric and magnetic fields, and applied to astrophysics, controlled fusion, accelerator physics and beam storage [3,4].…”

Section: Introductionmentioning

confidence: 99%

Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

et al. 2021

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A (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynam-ics and plasma physics is hereby investigated. Via the Hirota method, bilinear Bäcklund transformation are obtained, along with two types of the analytic solutions. Kink-shaped soliton solutions are derived via the Hirota method. Breather solutions are derived via the extended homoclinic test approach and lump solutions are obtained from the breather solutions under a limiting procedure. We find that the shape and amplitude of the one-kink soliton keep unchanged during the propagation and the velocity of the one-kink soliton depends on all the coefficients in the equation. We graphically demonstrate that the interaction between the two-kink solitons is elastic, and analyse the solitons with the influence of the coefficients. We observe that the amplitudes and shapes of the breather and lump remain unchanged during the propagation, and graphically present the breathers and lumps with the influence of the coefficients in the equation.

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Solitons and periodic waves for the (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Cited by 88 publications

References 59 publications

Resonance Y-shape solitons and mixed solutions for a (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Resonance Y-shape solitons and mixed solutions for a (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

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

Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

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