Kink, breather and asymmetric envelope or dark solitons in nonlinear chains. I. Monatomic chain

Flytzanis, N.; Pnevmatikos, St.; Remoissenet, M.

doi:10.1088/0022-3719/18/24/009

Cited by 133 publications

(42 citation statements)

References 30 publications

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“…However for the case v 2 = 0 a more restrictive condition is obtained by demanding Consequently for an acoustic spectrum case the condition -that the band edge plane wave frequency is repelled from the linear spectrum with increasing amplitude -is only necessary but not sufficient for a tangent bifurcation to occur. It is interesting to note that condition (10.22) has been obtained with the help of multiple scale expansions already in 1972 by Tsurui [184] and more recently by Flytzanis, Pnevmatikos and Remoissenet [92] for systems with v µ = 0.…”

Section: The Case φ2m+1 =mentioning

confidence: 89%

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Discrete breathers

1998

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Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices -quantum breathers.Finally we will formulate a new conceptual aproach capable of predicting whether discrete breather exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.

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Section: The Case φ2m+1 =mentioning

confidence: 89%

“…Modulational instability has been analyzed for lattices with respect to discrete breathers in a number of publications by Kivshar and Peyrard [125], Flytzanis, Pnevmatikos and Remoissenet [92], Tsurui [184] and Sanduski and Page [156].…”

Section: Plane Wave Bifurcations and Discrete Breathersmentioning

confidence: 99%

Discrete breathers

1998

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“…µÚÇÕ ÄÊÂËÏÑAEÇÌÔÕÄËâ ÄÕÑÓÞØ ÔÑÔÇAEÇÌ AEÂÉÇ Ä ÑAEÐÑ-ÏÇÓÐÑÌ ÏÑAEÇÎË [33,34] µAEÑÃÐÑ ÑÕ ÂÃÔÑÎáÕÐÞØ ÍÑÑÓAEËÐÂÕ n-ÅÑ ÊÄÇÐÂ x n , y n ÒÇÓÇÌÕË Í ÃÇÊÓÂÊÏÇÓÐÞÏ ÑÕÐÑÔËÕÇÎßÐÞÏ ÍÑÑÓAEËÐÂÕÂÏ …”

Section: £äçAeçðëçunclassified

Nonlinear dynamics of zigzag molecular chains

Savin¹,

Manevich²,

Christiansen³

et al. 1999

Usp. Fiz. Nauk

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“…These localized non-dispersive travelling waves can be of several distinct types [5], such as kink, pulse, breather, envelope, and dark solitons, all of them presenting the property that their shapes and velocities are preserved along propagation, and even upon collision with other solitary waves. In fact, they result from a precise balance among the competing elements that define the equation, namely the tendency of spreading due to the presence of a dispersive term and the action of nonlinear terms, which in general favour large amplitude disturbances and velocities that assure the stability of the travelling waves with respect to small distortions in form.…”

Section: Introductionmentioning

confidence: 99%

“…In the continuum spatial limit, the longitudinal displacement of the particle n from its equilibrium position, u n (t), is replaced by an analytic function u(x, t), and the series expansion of the interaction terms gives rise to the spatial derivatives of high orders. In this context, A(u) thus represents an on-site local interaction potential in the differential equation of motion that governs the system [5].…”

Section: Introductionmentioning

confidence: 99%

Exact kink solitons in the presence of diffusion, dispersion, and polynomial nonlinearity

Raposo

Bazeia

1999

Physics Letters A

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We describe exact kink soliton solutions to nonlinear partial differential equations in the generic form u t + P (u)u x + νu xx + δu xxx = A(u), with polynomial functions P (u) and A(u) of u = u(x, t), whose generality allows the identification with a number of relevant equations in physics. We emphasize the study of chirality of the solutions, and its relation with diffusion, dispersion, and nonlinear effects, as well as its dependence on the parity of the polynomials P (u) and A(u) with respect to the discrete symmetry u → −u. We analyze two types of kink soliton solutions, which are also solutions to 1 + 1 dimensional φ 4 and φ 6 field theories.

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Kink, breather and asymmetric envelope or dark solitons in nonlinear chains. I. Monatomic chain

Cited by 133 publications

References 30 publications

Discrete breathers

Discrete breathers

Nonlinear dynamics of zigzag molecular chains

Exact kink solitons in the presence of diffusion, dispersion, and polynomial nonlinearity

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