Multi-pole solutions and their asymptotic analysis of the focusing Ablowitz–Ladik equation

Li, Min; Yue, Xiaolu; Xu, Tao

doi:10.1088/1402-4896/ab4503

Cited by 18 publications

(4 citation statements)

References 50 publications

(96 reference statements)

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“…5 and 6. Asymptotic analysis on Solutions (24) has been proceeded, from which we have calculated the six asymptotic solitons as Asymptotic Solitons ( 25), ( 26) and (27). It has been shown that the characteristic lines of the one soliton component are η ± ln Asymptotic analysis on Solutions (24) has shown that the interactions among the second-order degenerate solitons component and one soliton component are elastic.…”

Section: Discussionmentioning

confidence: 99%

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N-fold generalized Darboux transformation and asymptotic analysis of the degenerate solitons for the Sasa-Satsuma equation in fluid dynamics and nonlinear optics

Gao

Ding

2023

Nonlinear Dyn

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In this paper, the Sasa-Satsuma equation, which is applied to the dynamics of the deep water waves, and the pulse propagation in the optical fibers and generally in the dispersive nonlinear media, is investigated. Starting from the first-order Darboux transformation, we construct an N -fold generalized Darboux transformation (GDT) for the Sasa-Satsuma equation, where N is a positive integer. Through the obtained N -fold GDT, we derive three kinds of the semirational solutions, which describe the second-order degenerate solitons, the third-order degenerate solitons, and the interaction between the second-order degenerate solitons and one soliton, respectively. We graphically illustrate the above three kinds of semirational solutions and investigate them through the asymptotic analysis, from which we find that the characteristic lines of the semirational solutions are composed of the straight lines and curves. Expressions of the characteristic lines, positions, amplitudes, slopes, positions and phase shifts of the asymptotic solitons are presented through the asymptotic analysis.

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Section: Discussionmentioning

confidence: 99%

“…Motivated by Refs. [27,28], we will perform the following asymptotic analysis procedure to investigate the asymptotic behaviors of Solutions (13).…”

Section: The Second-order Degenerate Solitons For Eq (1)mentioning

confidence: 99%

N-fold generalized Darboux transformation and asymptotic analysis of the degenerate solitons for the Sasa-Satsuma equation in fluid dynamics and nonlinear optics

Gao

Ding

2023

Nonlinear Dyn

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“…Up to now, a number of integrable nonlinear evolution equations have been derived to describe various nonlinear wave phenomena, like the solitons, breathers and rogue waves [1][2][3][4][5][6]. As a universe integrable model, the nonlinear Schrödinger equation (NLSE) appears in optics [7], fluids [8], plasmas [9], quantum field theory [10], Bose-Einstein condensates [11], etc.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the soliton solutions for a complex modified Korteweg–de Vries equation by a finite difference method

Xu¹,

Zhang²,

Wang³

et al. 2021

Commun. Theor. Phys.

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In this paper, a Crank–Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modified Korteweg–de Vries (MKdV) equation (which is equivalent to the Sasa–Satsuma equation) with the vanishing boundary condition. It is proved that such a numerical scheme has the second-order accuracy both in space and time, and conserves the mass in the discrete level. Meanwhile, the resulting scheme is shown to be unconditionally stable via the von Nuemann analysis. In addition, an iterative method and the Thomas algorithm are used together to enhance the computational efficiency. In numerical experiments, this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation. The numerical accuracy, mass conservation and linear stability are tested to assess the scheme’s performance.

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“…Studying the solutions of nonlinear evolution equations is a direct method to understand the nonlinear evolution equations. All the time, the study of new solution is a hot topic in the research field, such as the soliton interactions [1,2], nonlocal solutions [3] and so on.…”

Section: Introductionmentioning

confidence: 99%

The interaction among kink, breather and lump in the (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation

Wang

Zhaqilao

2020

Phys. Scr.

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A (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation is studied. Based on the Hirota bilinear method, multi-kink solutions are obtained. The higher-order lump solutions are obtained by the long-wave limit approach. By selecting the complex conjugate parameters conditions for multi-kink solutions, the multi-breather solutions are constructed. Moreover, ten kinds of interaction solutions consisted of three waves for kink, breather and lump are obtained. Some dynamical behaviors of the solutions obtained in the paper are shown by figures.

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Multi-pole solutions and their asymptotic analysis of the focusing Ablowitz–Ladik equation

Cited by 18 publications

References 50 publications

N-fold generalized Darboux transformation and asymptotic analysis of the degenerate solitons for the Sasa-Satsuma equation in fluid dynamics and nonlinear optics

N-fold generalized Darboux transformation and asymptotic analysis of the degenerate solitons for the Sasa-Satsuma equation in fluid dynamics and nonlinear optics

Numerical simulation of the soliton solutions for a complex modified Korteweg–de Vries equation by a finite difference method

The interaction among kink, breather and lump in the (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation

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