Solitary waves, breathers, and rogue waves modulated by long waves for a model of a baroclinic shear flow

In this paper, a (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada system is investigated in fluid mechanics via the symbolic computation. With the help of the Hirota method, we derive some singular soliton, shock-wave, breather-stripe soliton and hybrid solutions. Based on the finite difference method, we get some numerical one-soliton solutions. We graphically show the singular and shock-wave solutions, and observe that the singular one-soliton solutions are explosive and unstable, but the shock-wave solutions are nonsingular and stable. We observe that the breatherstripe soliton moves along the negative direction of the y axis, where y is a variable, and the amplitude and shape of the breather-stripe soliton remain invariant during the propagation. We graphically demonstrate the interaction among a rogue wave, a periodic wave and a pair of the stripe solitons: the rogue wave arises from the one stripe soliton; the rogue wave interacts with the periodic wave, the rogue wave splits into two waves and then the two waves merge into a wave; the rogue wave fuses with the other stripe soliton. We graphically present the numerical one-soliton solutions which agree with the analytic one-soliton solutions.

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“…Figs. 4 show the interaction among a rogue wave, a periodic wave and a pair of the stripe solitons via Solutions (15). In Figs.…”

Section: Breather-stripe Soliton Solutions For System (1)mentioning

confidence: 99%

Singular soliton, shock-wave, breather-stripe soliton, hybrid solutions and numerical simulations for a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system in fluid mechanics

Liu

Tian

2022

Nonlinear Dyn

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“…Assuming g j = ϕ j = 0, ðj = 3, 4,⋯Þ, it is easy to see that Equation (10) and other equations from the coefficients of parameter ε are satisfied automatically. So we obtain the following one-soliton solution for the general coupled KdV Equation (2) by setting ε = 1 :…”

Section: The Bilinear Form and Soliton Solutionsmentioning

confidence: 99%

“…In the soliton theory, finding the soliton solutions for the nonlinear partial equations is becoming more and more important since the soliton solutions can describe many complex physical phenomena [1]. Many effective approaches have been proposed, such as the inverse scattering transformation method [2], the Bäcklund transformation method [3], the Darboux transformation method [4][5][6], the Hirota bilinear method [7][8][9][10][11], and the Riemann-Hilbert method [12]. Among them, the Hirota bilinear method is not only direct but also effective for investigating the soliton solutions.…”

Section: Introductionmentioning

confidence: 99%

The Soliton Solutions and Long-Time Asymptotic Analysis for a General Coupled KdV Equation

Zhang

Chen

2021

Advances in Mathematical Physics

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A general coupled KdV equation, which describes the interactions of two long waves with different dispersion relation, is considered. By employing the Hirota’s bilinear method, the bilinear form is obtained, and the one-soliton solution and two-soliton solution are constructed. Moreover, the elasticity of the collision between two solitons is proved by analyzing the asymptotic behavior of the two-soliton solution. Some figures are displayed to illustrate the process of elastic collision.

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“…Relevant soliton issues can be seen in Refs. [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In the multimode and birefringent fibers, vector optical solitons for the coupled NLS (CNLS) equations have been considered in two (or more) field components with different frequencies or polarizations [29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Vector solitons for the (2 + 1)‐dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber

Sun

Tian

et al. 2021

Z Angew Math Mech

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Investigated in this paper is the (2 + 1)-dimensional coupled nonlinear Schrödinger system, which describes the propagation of the optical soliton through the Kerr nonlinear fiber in which each component diffracts in two transverse dimensions. By virtue of the Kadomtsev-Petviashvili hierarchy reduction, we obtain the bright, dark and mixed vector soliton solutions in terms of the Gramian. We investigate the vector solitons graphically: (1) Bright-dark one solitons with one of the components being gray or black are shown. Bouncing, beating, oscillating and breathing effects which appear during the interactions between the bright-dark two solitons are discussed, and those interactions are shape-preserving; (2) Degenerate and non-degenerate dark-dark one solitons are presented. Interaction of the dark-dark two solitons is discussed and the two solitons keep their amplitudes and velocities invariant except for some phase shifts during the interaction; (3) Bound-state and complexes of the bright-bright solitons are presented.

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Solitary waves, breathers, and rogue waves modulated by long waves for a model of a baroclinic shear flow

Cited by 87 publications

References 59 publications

Singular soliton, shock-wave, breather-stripe soliton, hybrid solutions and numerical simulations for a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system in fluid mechanics

Singular soliton, shock-wave, breather-stripe soliton, hybrid solutions and numerical simulations for a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system in fluid mechanics

The Soliton Solutions and Long-Time Asymptotic Analysis for a General Coupled KdV Equation

Vector solitons for the (2 + 1)‐dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber

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