Dynamics of nondegenerate vector solitons in a long-wave–short-wave resonance interaction system

Stalin, S.; Ramakrishnan, R.; Lakshmanan, M.

doi:10.1103/physreve.105.044203

Cited by 19 publications

(5 citation statements)

References 60 publications

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“…Thus, a new class of fundamental bright solitons, namely nondegenerate fundamental vector bright solitons, can be obtained. The nondegenerate soliton solution of nonlinear integrable equations is a very interesting and important issue, which had been explored by many scholars recently [27,28,29]. We argue that this phenomenon is equally presented in the fcHirota equation.…”

Section: Introductionmentioning

confidence: 74%

Nondegenerate solitons in the integrable fractional coupled Hirota equation

An¹,

Ling²,

Zhang³

2022

Preprint

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In this paper, based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr in the sense of Riesz fractional derivative, we explore the fractional coupled Hirota equation and give its explicit form. Unlike the previous nonlinear fractional equations, this type of nonlinear fractional equation is integrable. Therefore, we obtain the fractional n-soliton solutions of the fractional coupled Hirota equation by inverse scattering transformation in the reflectionless case. In particular, we analyze the one-and twosoliton solutions of the fractional coupled Hirota equation and prove that the fractional two-soliton can also be regarded as a linear superposition of two fractional single solitons as |t| → ∞. Moreover, under some special constraint, we also obtain the nondegenerate fractional soliton solutions and give a simple analysis for them.

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Section: Introductionmentioning

confidence: 74%

Nondegenerate solitons in the integrable fractional coupled Hirota equation

An¹,

Ling²,

Zhang³

2022

Preprint

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“…(i) When p 1I = p 2I , the solutions ( 22) in all components (u (1) , u (2) , v) only comprise nondegenerate solitons with profiles of double-or single-hump localized structures, which are designated as (1, 1, 1)-soliton [61]. Particularly, these nondegenerate solitons in u (1) , u (2) , and v components have identical velocities, which are 2p 1I .…”

Section: The Fundamental Non-degenerate Solitonsmentioning

confidence: 99%

Dynamics of degenerate and nondegenerate solitons in the two-component nonlinear Schrödinger equations coupled to Boussinesq equation

2022

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The paper studies the dynamics of degenerate and nondegenerate bright solitons and their collisions in the two-component nonlinear Schrödinger equations coupled to Boussinesq equation. The degenerate solitons that have only singlehump profiles, exhibit both elastic and inelastic collisions, and their velocities are identical in the two short wave (SW) components and in the long wave (LW) component. The nondegenerate single solitons have two different forms: one of them has double-or single-hump profiles and identical velocities in all SW and LW components, and the other one only admits single-hump profiles and has unequal velocities in the two SW components. The collisions of nondegenerate solitons cannot result in the redistribution of soliton intensities. Three different types of collisions of nondegenerate two-soliton solutions are studied in detail. KeywordsNondegenerate solitons • Soliton collisions • Two-component nonlinear Schrödinger equations coupled to Boussinesq equation • Bilinear KP-reduction method.

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“…Breathers usually include the Akhmediev breather (AB), Kuznetsov-Ma breather and spatio-temporally periodic breather based on its evolutionary directions. Localized waves are widespread in nonlinear evolution equations, hence, obtaining them theoretically has piqued the interest of academics [21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics

Wang,

Zhou,

Yang

et al. 2023

Proc. R. Soc. A.

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This paper investigates a higher-order modified nonlinear Schrödinger equation with higher-order dispersion and self-steepening effects, which can be used to study the dynamics of asymmetric and steepened optical pulse transmission in optical fibres. The modulation instability of the plane-wave solution has been analysed, and the state transition of the rogue waves under the higher-order dispersion effect is presented. The findings demonstrate that the self-steepening effect may also produce an asymmetric unstable frequency band. Combined with the modulation instability, the rogue wave, rational soliton and mixed interaction of localized waves have a quantitative relationship with plane-wave parameters. Various exact solutions can be accurately located and obtained according to the generalized Darboux transformation. The asymptotic analysis of rational solutions demonstrates the state transition of higher-order rogue waves. This paper illustrates the significance of modulation instability for studying the integrable systems by the Darboux transformation. It is a new guidance to solve the difficulty of exact excitation of asymmetric localized waves in complex integrable systems. The results have prospective applications and references for the emergence, amplification and compression of asymmetric pulses in optical experiments.

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Dynamics of nondegenerate vector solitons in a long-wave–short-wave resonance interaction system

Cited by 19 publications

References 60 publications

Nondegenerate solitons in the integrable fractional coupled Hirota equation

Nondegenerate solitons in the integrable fractional coupled Hirota equation

Dynamics of degenerate and nondegenerate solitons in the two-component nonlinear Schrödinger equations coupled to Boussinesq equation

Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics

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