Breather wave solutions for the generalized shallow water wave equation with variable coefficients in the atmosphere, rivers, lakes and oceans

Liu, Jian-Guo; Zhu, Wen‐Hui

doi:10.1016/j.camwa.2019.03.008

Cited by 46 publications

(15 citation statements)

References 27 publications

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“…Liu and Zhu [25] investigated the variable coefficients of the gSW equation by the Hirota bilinear method and constructed a large number of breather wave solutions. Tang, Ma and Xu [26] proposed the (3 + 1)-dimensional generalized Shallow Water-like (gSWl) equation…”

Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

Yang

Song²,

Wang³

2023

Front. Phys.

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In this article, (3+1)-dimensional generalized Shallow Water-like (gSWl) equation is discussed. The infinitesimal generators of the equation are derived by using the Lie symmetry analysis method. The optimal system is obtained based on the adjoint table of the generators of the equation. Exact solutions of the equation are constructed by applying symmetry reduction, Exp−ϕ(ξ) expansion method, Exp-function expansion method, Riccati equation method, and G′/G expansion method. For analyzing the dynamical behavior of the solutions, we derive the physical structures of dark soliton, kink wave, and periodic solutions via numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

Yang

Song²,

Wang³

2023

Front. Phys.

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“…Nonlinear evolution equations (NLEEs) have been proposed to model certain nonlinear phenomena in nonlinear optics, fluid mechanics, plasma physics, etc [16][17][18][19][20][21][22]. As some NLEEs, shallow-water equations have been used to depict the horizontal structure of an atmosphere and the evolution of an incompressible fluid [23]. There have been some methods to solve the NLEEs, including the Lie symmetry approach, Bäcklund transformation, Darboux transformation, Hirota method, and so on [24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

X-type Soliton, Resonance Y-type Soliton and Hybrid Solutions of a (2+1)-dimensional Hirota-Satsuma-Ito System for the Shallow Water Waves

Shen

Tian

Zhou

et al. 2021

Preprint

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Water waves are observed in the rivers, lakes, oceans, etc. Under investigation in this paper is a (2+1)-dimensional Hirota-Satsuma-Ito system arising in the shallow water waves. Via the Hirota method and symbolic computation, we derive some X-type and resonance Y-type soliton solutions. We also work out some hybrid solutions consisting of the resonance Y-type solitons, solitons, breathers and lumps. Graphics we present reveal that the hybrid solutions consisting of the resonance Y-type solitons and solitons/breathers/lumps describe the interactions between the resonance Y-type solitons and solitons/breathers/lumps, respectively. The obtained results rely on the water-wave coefficient in that system.

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“…Huang et al [37] have given the bilinear Bäcklund transformation, soliton, and periodic wave solutions for equation (2). Liu and Zhu [38] have studied the breather wave solutions of equation (2). However, to our knowledge, the lump wave solutions and their nonautonomous characteristics (e.g., the accelerated and decelerated motions and trajectories) have not been reported yet.…”

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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Breather wave solutions for the generalized shallow water wave equation with variable coefficients in the atmosphere, rivers, lakes and oceans

Cited by 46 publications

References 27 publications

Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

X-type Soliton, Resonance Y-type Soliton and Hybrid Solutions of a (2+1)-dimensional Hirota-Satsuma-Ito System for the Shallow Water Waves

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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