Inverse scattering transform for the Yajima-Oikawa equations with nonvanishing boundary conditions

Заболотский, А. А.

doi:10.1103/physreva.80.063616

Cited by 31 publications

(18 citation statements)

References 21 publications

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“…The detailed dynamics of soliton collisions described by two-soliton solution (21) can be explored by analyzing the solution [18,19,43,44] in asymptotic limits. In this section, we discuss the collision among two bright solitons of the 2-component YO system comprising two short waves and a long wave.…”

Section: Soliton Collisionsmentioning

confidence: 99%

“…Recent studies also indicate that the multicomponent YO system will find promising applications in condensed matter theory, particularly in spinor condensates [21]. More interestingly, in a classic work [22], multicomponent YO-type equations have been derived in the context of the many-component magnonphonon system and its corresponding Hamiltonian formalism was developed, but the complete dynamics of solitons in such system still remains unexplored.…”

Section: Introductionmentioning

confidence: 99%

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General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions

Kanna¹,

Sakkaravarthi²,

Tamilselvan³

2013

Phys. Rev. E

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We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N -soliton solution of the multicomponent YO system in the Gram determinant form by using Hirotas bilinearization method and explicitly analyze the one-and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients.We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

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Section: Soliton Collisionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions

Kanna¹,

Sakkaravarthi²,

Tamilselvan³

2013

Phys. Rev. E

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“…NLSWIS's are not only rich complex models for strong nonlinearities, but also represent the constitutive prototypes for highly interesting interaction phenomena, emanating from various applications, such as gravity and water waves, plasma and bio-physics, as well as nonlinear optics, to name a few, [3]. For instance, long gravity wave and Manuscript Click here to view linked References 2 capillary-gravity wave for finite-depth water interactions findings by Grimshaw in [4] are of major significance.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for nonlinear long–short wave interaction systems with highly complex structure

Baskonus

Belgacem

2017

Journal of Computational and Applied Mathematics

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Sunday, May 27, 2016]In this paper, we investigate and use the new modified exp     -Ωξ -expansion method, (MEM). We apply the new MEM to nonlinear long short-wave interactions systems (NLSWIS).Among our findings are sets of solutions including, but not limited to, new hyperbolic, complex, and dark soliton solutions. Not only is MEM shown to be highly adaptable for partial differential equations with strong nonlinearities, but also, it turns out to be highly efficient, despite its ease.

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“…The theoretical investigation of this nonlinear resonance interaction originated from the study of the dynamics of Langmuir and ion acoustic waves in plasma by Zakharov . In the case of LW propagating in only one direction, the Zakharov system reduces to the Yajima–Oikawa (YO) system

i {\overset{S}{true}}_{t} + {\overset{S}{true}}_{x x} + \hat{S} \hat{L} = 0,

{\overset{L}{true}}_{t} = 2 σ false(false| \hat{S} {{false|}^{2})}_{x}, σ^{2} = 1,

which was shown to be integrable by using inverse scattering transform (IST) and admits multisoliton solutions .…”

Section: Introductionmentioning

confidence: 99%

The Derivative Yajima–Oikawa System: Bright, Dark Soliton and Breather Solutions

et al. 2018

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In this paper, we study the derivative Yajima–Oikawa (YO) system which describes the interaction between long and short waves (SWs). It is shown that the derivative YO system is classified into three types which are similar to the ones of the derivative nonlinear Schrödinger equation. The general N‐bright and N‐dark soliton solutions in terms of Gram determinants are derived by the combination of the Hirota's bilinear method and the Kadomtsev–Petviashvili hierarchy reduction method. Particularly, it is found that for the dark soliton solution of the SW component, the magnitude of soliton can be larger than the nonzero background for some parameters, which is usually called anti‐dark soliton. The asymptotic analysis of two‐soliton solutions shows that for both kinds of soliton only elastic collision exists and each soliton results in phase shifts in the long and SWs. In addition, we derive two types of breather solutions from the different reduction, which contain the homoclinic orbit and Kuznetsov–Ma breather solutions as special cases. Moreover, we propose a new (2+1)‐dimensional derivative Yajima–Oikawa system and present its soliton and breather solutions.

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Inverse scattering transform for the Yajima-Oikawa equations with nonvanishing boundary conditions

Cited by 31 publications

References 21 publications

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions

Analytical solutions for nonlinear long–short wave interaction systems with highly complex structure

The Derivative Yajima–Oikawa System: Bright, Dark Soliton and Breather Solutions

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