Wick-type stochastic multi-soliton and soliton molecule solutions in the framework of nonlinear Schrödinger equation

Han, Haobin; Li, Huijun; Dai, Chao-Qing

doi:10.1016/j.aml.2021.107302

Cited by 34 publications

(9 citation statements)

References 15 publications

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“…In [40], Dai et al investigated scalar and vector rogue waves in a partially nonlocal nonlinear medium with linear and harmonic potentials. In addition, [41,42] studied wick-type stochastic multi-solitons, soliton molecules, and fractional soliton solutions of the NLSE. In [43], vector breathers for the coupled fourth-order NLSE were investigated.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of breathers and rogue waves in scalar and multicomponent nonlinear systems

Wang¹,

Wang²

2022

Commun. Theor. Phys.

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In this paper, a new method, the variable separation technique, for seeking breather and rogue wave solution to nonlinear evolution equation is proposed. Integrable systems of derivative nonlinear Schr\"{o}dinger type are used as three examples to illustrate the effectiveness of the presented method. Then we obtain a family of rational solutions. This family of solutions includes Akhmediev breather, Kuznetsov-Ma breather, versatile rogue waves, various interactions of localized waves. Moreover, the main characteristics of these solutions are discussed with some graphics. More importantly, our results show that more abundant and novel localized waves may exist in the multi-component coupled equations than in the uncoupled ones.

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Section: Introductionmentioning

confidence: 99%

Dynamics of breathers and rogue waves in scalar and multicomponent nonlinear systems

Wang¹,

Wang²

2022

Commun. Theor. Phys.

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“…It is common knowledge that the exact solutions of nonlinear partial differential equations are of great significance in the fields of fluids, optics, Bose-Einstein condensate and plasmas, since they can provide valuable physical information and give deep understandings for some nonlinear wave phenomena [1][2][3][4][5][6][7][8][9]. Types of nonlinear wave include solitons [10], rogue waves [11], Akhmediev breathers [12], Kuznetsov-Ma breathers [13][14][15], superregular breathers [16,17] and lump waves [18][19][20][21][22][23][24][25][26][27][28], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Shape-changed propagations and interactions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluids

Zhang¹,

Wang²,

Liu³

et al. 2021

Commun. Theor. Phys.

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In this article, we consider the (3+1)-dimensional generalized Kadomtsev–Petviashvili (GKP) equation in fluids. We show that a variety of nonlinear localized waves can be produced by the breath wave of the GKP model, such as the (oscillating-) W- and M-shaped waves, rational W-shaped waves, multi-peak solitary waves, (quasi-) Bell-shaped and W-shaped waves and (quasi-) periodic waves. Based on the characteristic line analysis and nonlinear superposition principle, we give the transition conditions analytically. We find the interesting dynamic behavior of the converted nonlinear waves, which is known as the time-varying feature. We further offer explanations for such phenomenon. We then discuss the classification of the converted solutions. We finally investigate the interactions of the converted waves including the semi-elastic collision, perfectly elastic collision, inelastic collision and one-off collision. And the mechanisms of the collisions are analyzed in detail. The results could enrich the dynamic features of the high-dimensional nonlinear waves in fluids.

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“…Indeed, the nature we live in operates in fractional dynamics, and it is simply for our own convenience that people use integer‐order models to describe complex nature 10 . In last several years, a large number of nonlinear models in technics and science have been spread to the fractional order derivative as to more explain physical and problems in daily life, 11–13 including polymers, viscoelastic materials, non‐Brownian motion, signal processing, and finance 14–17 …”

Section: Introductionmentioning

confidence: 99%

“…10 In last several years, a large number of nonlinear models in technics and science have been spread to the fractional order derivative as to more explain physical and problems in daily life, [11][12][13] including polymers, viscoelastic materials, non-Brownian motion, signal processing, and finance. [14][15][16][17] In recent studies, NDDEs are generalized to the corresponding forms with the fractional order derivative. 18,19 The fractional NDDEs (FNDDEs) play an significant role in the application of physics, chemistry, biology, engineering, and so on.…”

Section: Introductionmentioning

confidence: 99%

Discrete soliton solutions of the fractional discrete coupled nonlinear Schrödinger equations: Three analytical approaches

Wang

Dai

2021

Math Methods in App Sciences

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The fractional discrete coupled nonlinear Schrödinger equations are solved on account of the modified Riemann–Liouville fractional derivative and Mittag–Leffler function. By using the fractional generalized Riccati method, generalized Mittag–Leffler function method and fractional generalized tanh–sech function method, some new analytical discrete solutions constructed by generalized trigonometric and hyperbolic functions are obtained, including discrete fractional bright soliton, dark soliton, combined soliton, and periodic solutions. In order to illustrate the effect of fractional order parameter on dynamics of fractional discrete soliton, some results in this study are illustrated graphically. Results indicate that although the combined wave is made up of singular coth function, it does not exhibit the singular property in the discrete case. Moreover, two kinds of scalar soliton solutions are found. These results could be of great significance to further study complex nonlinear discrete physical phenomena.

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Wick-type stochastic multi-soliton and soliton molecule solutions in the framework of nonlinear Schrödinger equation

Cited by 34 publications

References 15 publications

Dynamics of breathers and rogue waves in scalar and multicomponent nonlinear systems

Dynamics of breathers and rogue waves in scalar and multicomponent nonlinear systems

Shape-changed propagations and interactions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluids

Discrete soliton solutions of the fractional discrete coupled nonlinear Schrödinger equations: Three analytical approaches

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