Soliton Solutions in a Diatomic Lattice System

Yajima, Nobuo; Satsuma, Junkichi

doi:10.1143/ptp.62.370

Cited by 107 publications

(32 citation statements)

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“…Benney [5,6], Grimshaw [17], Djordjevic and Redekopp [12], and Yajima and Satsuma [42] studied these systems numerically. We show that the solution of the system (1.3) is locally well-posed in the space H s (R)_H s&1Â2 (R) (s 0).…”

Section: Introductionmentioning

confidence: 99%

Interaction Equations for Short and Long Dispersive Waves

Bekiranov

Ogawa

Ponce

1998

Journal of Functional Analysis

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Section: Introductionmentioning

confidence: 99%

Interaction Equations for Short and Long Dispersive Waves

Bekiranov

Ogawa

Ponce

1998

Journal of Functional Analysis

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“…The system is characterized by three dimensionless parameters: the particle mass m, the anharmonicity of the chain α, and the dispersion coefficient µ. Equation (1) appears in a number of other physical contexts including, for example, the interaction of nonlinear electron-plasma and ion-acoustic waves [9], coupled Langmuir and ion-acoustic plasma waves [10], interaction of optical and acoustic modes in diatomic lattices [11], particle theory models [12], etc.System (1) is known to be integrable for αµ = 6 [13]. In this case, it possesses two types of single-soliton solutions: scalar (ψ = 0) supersonic Boussinesq (Bq) solitons and vector Davydov-Scott (DS) solitons [8] which can be both subsonic and supersonic.…”

mentioning

confidence: 99%

Multi-soliton energy transport in anharmonic lattices

Ostrovskaya¹,

Mingaleev²,

Kivshar³

et al. 2001

Physics Letters A

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We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons [see Phys. Rev. Lett. 83, 296 (1999)], our analysis reveals a novel physical mechanism for the formation of stable multihump solitary waves in nonintegrable multi-component nonlinear models.Spatially localised solutions of multi-component nonlinear models, multi-component solitary waves, have received a great deal of attention in the last decade. In particular, recent studies in the nonlinear optics [1,2] and Bose-Einstein condensation [3] have shown that, under certain conditions and only in multi-component systems, the formation of dynamically stable localized states and soliton complexes is possible. Unlike their singlecomponent (or scalar) counterparts, multi-component (or vector) solitons possess complex internal structure forming a kind of "soliton molecules", which makes them attractive, both from the fundamental and applied point of view, as composite and reconfigurable carriers for a transport of spatially localized energy.Recent discovery of stable multi-component spatial solitons in optics [1,2] shed a light on the general physical mechanisms of the formation and stability of multicomponent localised states. Such states are often called multihump solitons due to multiple maxima displayed in their intensity profile. Usually, multihump solitary waves appear via bifurcations of scalar solitons when a primary soliton plays a role of an effective waveguide ("potential well") that traps higher-order guided modes excited in a complimentary field [2]. On the other hand, the multihump solitons can be formed as multi-soliton bound states, when two or more different vector solitons are "glued" together due to balanced interaction between the soliton constituents [4].Soliton bifurcations and binding enable the existence of multi-component localized states in many nonlinear models; these include bound states of dark solitons [4] and incoherent solitons [5] in optics, and multihump plasma waves [6]. Importantly, multihump solitary waves are also found in higher dimensions [6,7].The experimental and theoretical results on optical solitons [1,2] challenge the conventional view on multicomponent solitary waves in other fields of nonlinear physics. The main question we wish to address here is: Can stable multihump solitons exist in other important models of nonlinear physics? This is a crucial issue because, so far, the stable multihump solitons have been positively identified only in the nonlinear optical model of Refs. [1,2] that is known to possess additional symmetries, which might be the reason for their unique stability.In this Letter, we demonstrate the existence of dynamically stable multihump solitary states in a completely different (in both the physics and properties) but even more general model that describes the interaction of envelope and lattice excitations, a generalisation of the...

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“…What's more, the study on nonlinear systems describing the interaction of long waves with short wave packets in nonlinear dispersive media has received much attentions in recent years [11][12][13][14][15][16]. Such systems have found wide applications in the fields of hydrodynamics, nonlinear optics, plasma physics and so on [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Bright-Dark MixedN-Soliton Solution of Two-Dimensional Multicomponent Maccari System

Han

Chen

2017

Zeitschrift Für Naturforschung A

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By virtue of the KP hierarchy reduction technique, we construct the general bright-dark mixed N-soliton solution to the multi-component Mel'nikov system comprised of multiple (say M) short-wave components and one longwave component with all possible combinations of nonlinearities including all-positive, all-negative and mixed types. Firstly, the two-bright-one-dark (2-b-1-d) and one-bright-two-dark (1-b-2-d) mixed N-soliton solutions in short-wave components of the three-component Mel'nikov system are derived in detail. Then we extend our analysis to the M-component Mel'nikov system to obtain its general mixed N-soliton solution. The formula obtained unifies the allbright, all-dark and bright-dark mixed N-soliton solutions. For the collision of two solitons, the asymptotic analysis shows that for a M-component Mel'nikov system with M ≥ 3, inelastic collision takes place, resulting in energy exchange among the short-wave components supporting bright solitons only if the bright solitons appear at least in two short-wave components. Whereas, the dark solitons in the short-wave components and the bright solitons in the long-wave component always undergo elastic collision which just accompanied by a position shift.

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Soliton Solutions in a Diatomic Lattice System

Cited by 107 publications

References 1 publication

Interaction Equations for Short and Long Dispersive Waves

Interaction Equations for Short and Long Dispersive Waves

Multi-soliton energy transport in anharmonic lattices

Bright-Dark MixedN-Soliton Solution of Two-Dimensional Multicomponent Maccari System

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