Nonlinear superposition between lump and other waves of the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid dynamics

Ma, Hongcai; Yue, Shupan; Deng, Aiping

doi:10.1007/s11071-022-07508-1

Cited by 17 publications

(9 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As for the (2+1)-dimensional KdVSKR equation, few studies have been done on it, so many of its properties remain to be explored. Zhang et al [45][46][47] studied the process of nonlinear superposition of Kadomtsev-Petviashvili I equation, (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada equation and (2+1)-dimensional Sawada-Kotera equation. The (2+1)-dimensional KdVSKR equation has the similar property.…”

Section: Discussionmentioning

confidence: 99%

Novel y-type and hybrid solutions for the $$(2+1)$$-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Gao

Deng

2022

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

In this paper, the research object is (2+1)-dimensional KdVSKR equation. After adding new constraint, new solutions which contain y-type molecules are obtained. The process of lump molecules and y-type molecules before and after the collision is studied by long-wave limit method, and the kinetic behavior analysis is given. The interactions between y-type molecules and resonant soliton molecules, y-type molecules and breather molecules are obtained by combining velocity resonance method and mode resonance method, respectively. Finally, a novel hybrid solution containing lump molecule, breather molecule and y-type molecule is given, and the kinetic behavior is shown.

show abstract

Section: Discussionmentioning

confidence: 99%

Novel y-type and hybrid solutions for the $$(2+1)$$-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Gao

Deng

2022

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

show abstract

“…In (5), we consider the similarity transformations ψ(x, y, t) = ϕ(z, t), z = μ(t)x + σ (t)y, and t = t, where z and t are independent variables. Thus, (5) becomes…”

Section: The Model Equationmentioning

confidence: 99%

“…In [4], the 2D-CDGKSlike equation was investigated, based on bilinear neural network method, where novel solutions were derived. The N-soliton solutions were found by focusing on the nonlinear superposition between one lump and other types of localized waves of the2D-gCDGKSE [5]. 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].…”

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

View full text Add to dashboard Cite

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.

show abstract

“…The study of constructing solutions to nonlinear evolution equations (NLEEs) has received much attention [1][2][3][4][5][6][7][8][9]. NLEEs can be used to model various nonlinear waves in the nature [10][11][12][13][14][15][16][17][18]. A considerable number of NLEEs can be solved exactly in many ways, such as the inverse scattering method [19], the Bäcklund transformation [20] and the Hirota bilinear method [21].…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of the lump solutions and mixed solutions to a (2+1)-dimensional nonlinear model

Chen

Lü²,

Yin

2023

Commun. Theor. Phys.

View full text Add to dashboard Cite

In this paper, we propose a combined form of bilinear Kadomtsev-Petviashvili equation and the bilinear extended (2+1)-dimensional shallow water wave equation, which is linked with a novel (2+1)-dimensional nonlinear model. This model might be applied to describe the evolution of nonlinear waves in the ocean. Under the effect of a novel combination of nonlinearity and dispersionterms, two cases of lump solutions to the (2+1)-dimensional nonlinear model are derived by searching for the quadratic function solutions to the bilinear form. Moreover, the one-lump-multi-stripe solutions are constructed by the test function combining quadratic functions and multiple exponential functions. The one-lump-multi-soliton solutions are derived by the test function combiningquadratic functions and multiple hyperbolic cosine functions. Dynamic behaviors of the lump solutions and mixed solutions are analyzed via numerical simulation. The result is of importance to provide efficient expressions to model nonlinear waves and explain some interaction mechanism of nonlinear waves in physics.

show abstract

Nonlinear superposition between lump and other waves of the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid dynamics

Cited by 17 publications

References 52 publications

Novel y-type and hybrid solutions for the $$(2+1)$$-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Novel y-type and hybrid solutions for the $$(2+1)$$-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

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

Dynamic behaviors of the lump solutions and mixed solutions to a (2+1)-dimensional nonlinear model

Contact Info

Product

Resources

About