Multi-soliton energy transport in anharmonic lattices

Abstract

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...

Mobility of discrete multibreathers in the exciton dynamics of the Davydov model with saturable nonlinearities

“…We can conclude that the localization of vibrational energy in protein can be in the form of single discrete solitons or a discrete multisoliton. A similar result was obtained in the past in the context of two-component solitary waves [35].…”

Quantum tunneling of three-spine solitons through excentric barriers

“…The energy released by hydrolysis of a single adenosine triphosphate (ATP) molecule is experimentally measured to exceed 0.6 eV [43][44][45], which is sufficient to excite 3 amide I quanta, each of which has energy E 0 = 0.2 eV. Because the continuum approximation of Davydov's model [18,27,[46][47][48][49] leads to sech-squared soliton solutions, we have applied the metabolic energy of a single ATP molecule in the form of Q = 3 amide I exciton quanta spread initially over 5 or 7 peptide groups as a discretized sech-squared pulse given by a discrete set of quantum probability amplitudes 1 √ 3 e ıαω2 A 3,α e −3ıω1 , A 2,α e −2ıω1 , A 1,α e −ıω1 , A 0,α , A 1,α e ıω1 , A 2,α e 2ıω1 , A 3,α e 3ıω1 (18) with phase factor along the spines ω 1 = π 12 [49], phase factor laterally across the spines ω 2 = 2π 3 [24,27], and real amplitudes A i,α that were dependent on the initial spread over peptide groups. The choice of the initial spread to be over at least 5 peptide groups is justified by the chemical structure and dimensions of the hydrolyzed ATP molecule and the enhanced thermal stability predicted for the resulting solitons [27].…”

Soliton oscillations in the Zakharov-type system at arbitrary nonlinearity-dispersion ratio

“…Solitons in such a Zakharov system (ZS) were studied for the following cases: (i) for equal nonlinearity and dispersion coefficients of the LF wave ( and , respectively, see Sec. 2 below) ( / = 1), a two-component Davydov-Scott (DS) soliton was found [18,19]; oscillations of the HF component in which were investigated in [20]; (ii) for / ≠ 1, an asymptotic solution in the form of a multihump soliton, assuming a sufficiently small HF field amplitude in comparison to the LF one, was found in [14]; (iii) a localized steady state of the HF wave field was found, neglecting strictional action of the HF field on LF waves, given that there exists a LF solution in the form of a "depression" soliton [17]; (iv) new two-component solitons with two free parameters were found analytically in [21] in the asymptotic approximation for an arbitrary ratio of nonlinearity and dispersion ; and, finally, a one-parameter family of exact two-component solitons under the condition of relatively weak dispersion, < 3 , was found in [21].…”

“…The co-propagation of HF and LF waves is governed by Zakharov-type systems of equations, in which the HF wave field is described by a linear Schrödinger equation with an effective potential generated by the LF wave field [12][13][14]. For electromagnetic and Langmuir waves in plasmas, this potential corresponds to perturbations in the plasma density caused by ion-acoustic waves.…”