Thermal conductivity of nonlinear waves in disordered chains

We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity κ(T). We find indications for an asymptotic low-temperature κ ∼ T ⁴ and intermediate temperature κ ∼ T ² laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).     

Localized nonlinear waves in systems with time- and space-modulated nonlinearities

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr?dinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.     

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.     

Diffusive Toda chains in models of nonlinear waves in active media

A class of models of autowaves in the form of nonlinear diffusion equations, which are closely related to the Liouville equation and two-dimensionalized Toda chains, is investigated. Exact solutions of these equations are constructed and analyzed. A simple method for constructing diffusive Toda chain models from known basic models is proposed. Zh. éksp. Teor. Fiz. 114, 1897–1914 (November 1998)     

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic–quintic nonlinear Schr o¨dinger(CCQNLS) equations through the generalized Darboux transformation(DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higherorder localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions;(ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons;(iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α.These results further uncover some striking dynamic structures in the CCQNLS system.     

Energy transfer in weakly coupled nonlinear oscillator chains: Transition from a wandering breather to nonlinear self-trapping

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly moving: the periodic wandering of the low-amplitude breather between the chains, and the one-chain-localization of the high-amplitude breather. These two modes of coupled breathers can be mapped exactly onto two solutions of a pendulum equation, detached by a separatrix mode. We also show that these two regimes of the coupled breathers are similar, and are described by a similar pair of equations, to the two regimes in the nonlinear tunneling dynamics of two weakly coupled Bose-Einstein condensates. On the basis of this analogy, we predict a new tunneling mode of two weakly coupled Bose-Einstein condensates in which their relative phase oscillates around π/2 modulo π.     

Spin waves in linear magnetic chains

We have calculated the time-dependent spin-spin correlation function for the classical Heisenberg chain by computer simulation at a series of temperatures. The results show clearly the existence in the non-ordered system of spin-wave excitations at sufficiently low temperatures.     

Localized oscillator expansions of nuclear two-body wave functions

Harmonic oscillator expansions are applied to two-body systems simulating the deuteron, triton and alpha particle. Convergence rates in energies and wave functions can be significantly improved when the expansions are localized by first subtracting an approximate asymptotic wave function.     

Localized vibrational modes around solitons in coupled trans-polyacetylene chains

The effects of interchain coupling have been studied on the localized vibrational modes around a soliton in doped and photoexcited samples of trans-(CH)_x by using an extension of the SSH model in which two neighboring chains modeled individually by SSH Hamiltonian and coupled by an interchain electronic transfer term are considered. The electronic pinning is also included within this model. The localized modes obtained in the SSH model are split and their frequencies are shifted after turning on the interchain coupling. Furthermore, our result can account for the three strong infrared lines at 900, 1260 and 1370 cm^?1 along with a weaker peak at 1150 cm^? r in the optical absorption spectra of lightly doped samples.     

Localized bending waves in a transversely isotropic plate

The problem of bending waves localized near the free edge of a transversely isotropic plate is investigated using the Ambartsumian higher-order plate theory which takes account of the transverse shears generated by flexural deformation. Unlike the first-order Reissner-Mindlin theory, which also takes account of transverse shears, Ambartsumian's analysis does not demand that plane normal cross-sections remain plane during bending. Within this analysis the existence of localized bending waves in transversely isotropic plates is established, and solutions of the dispersion equation obtained for different values of the elastic parameters.The analysis of frequencies of localized bending waves shows that for thick plates the effect of anisotropy can be considerable. For the particular case of vibrations of a narrow plate, from the long wave approximation a new beam vibration equation of the Timoshenko type is obtained for a transversally isotropic plate.     

Pulse propagation in one-dimensional nonlinear chains

Summary Several numerical computations are carried out to investigate the effects of the propagation of pulses (solitons and quasi-solitons) in one-dimensional nonlinear chains. Numerical results concerning the Toda lattice and a Coulomb-like lattice are discussed and compared. We consider lattices both with and without defects.

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Riassunto Si studiano gli effetti della propagazione di solitoni e di quasi solitoni in reticoli non lineari unidimensionali usando procedure di calcolo numerico. Si considerano il reticolo di Toda ed un reticolo di tipo Coulomb sia in presenza che in assenza di difetti.

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Резюме Используя процедуру численных вычислеий, исследуются эффекты распространения импульсов (солитонов или квази-солитонов) в одномерных нелинейных цепях. Обсуждаются и сравниваются численные редультаты, относящиеся к решетке тода и решетке кулоновского типа. Мы рассматриваем решетки с и вез дефектов.

     

On nonlinear effects in magnetic chains

The effect of phonon unharmonism and nonlinearity in exchange integrals on soliton excitations in ferromagnetic chains in the classical and long-wave limit are studied. It has been first shown that the unharmonic effect leads to a system of coupled Boussinesque and nonlinear Schrödinger equations allowing two types of soliton solutions. The nonlinear effect on the other hand results nonlinear Schrödinger equation with saturable nonlinearity admitting stable solitons in higher dimensional models.     

Aging phenomena in nonlinear dissipative chains

We study the energy relaxation in a one-dimensional nonlinear lattice with dissipative couplings. After thermalisation of this system, the extremities of the chain are put in contact with a zero-temperature reservoir, showing the existence of surprising quasi-stationary states with non zero energy, tough the dissipative coupling is high. This strange behavior, due to long-lived nonlinear localized modes, induces stretched exponential relaxation laws. Furthermore, we observe a strong dependence on the waiting time t_w after the quench of the two-time intermediate correlation function C(t_w+t, t_w). This function can be scaled onto a master curve, similar to the case of spin or Lennard-Jones glasses.Received: 11 February 2003, Published online: 4 August 2003PACS: 05.20.-y Classical statistical mechanics - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

Quantized spin waves in antiferromagnetic Heisenberg chains

The quantized stationary spin wave modes in one-dimensional antiferromagnetic spin chains with easy axis on-site anisotropy have been studied by means of Landau-Lifshitz-Gilbert spin dynamics. We demonstrate that the confined antiferromagnetic chains show a unique behavior having no equivalent, neither in ferromagnetism nor in acoustics. The discrete energy dispersion is split into two interpenetrating n and n' levels caused by the existence of two sublattices. The oscillations of individual sublattices as well as the standing wave pattern strongly depend on the boundary conditions. Particularly, acoustical and optical antiferromagnetic spin waves in chains with boundaries fixed (pinned) on different sublattices can be found, while an asymmetry of oscillations appears if the two pinned ends belong to the same sublattice.     

Extended spin waves in aperiodic ferromagnetic chains

In this work, a one-dimensional quantum Heisenberg ferromagnet with aperiodic exchange couplings is considered. To produce an aperiodic distribution of exchange couplings, it is used a sinusoidal function whose phase φ varies as a power-law, φ∝n^ν, where n labels the positions along the chain. By using exact diagonalization, the spin-wave participation number and the local density of states are computed. The numerical calculations indicate that for 0 < ν < 1, this ferromagnetic system displays a phase of extended spin waves in the low-energy region. For ν > 1 all spin waves are localized except for the zero energy mode. By integrating the time-dependent Schr?dinger equation, the temporal evolution of the mean-square displacement of the wave-packet was followed. Associated with the emergence of extended spin waves, it was observed that the wave-packet mean-square displacement displays a ballistic spread.     

Density waves in strongly correlated quantum chains

We review exact numerical results for one-dimensional quantum systems with half-filled bands. The topics covered include Peierls transitions in Holstein, Fröhlich, Su-Schrieffer-Heeger, and Heisenberg models with quantum phonons, competing fermion-boson and fermion-fermion interactions, as well as symmetry-protected topological states in fermion and anyon models.     

Charge-density waves in self-assembled halogen-bridged metal chains

Self-assembled growth of an ordered layer of Pt-Br-Pt chains on a Pt(110) surface is demonstrated. Upon slight doping with excess bromine, charge-density wave (CDW) domains separated by well-localized solutions are observed in the Br/Pt layer by scanning tunneling microscopy. Depending on annealing and adatom concentration, a global, long-range-ordered CDW ground state can be established. Angle-resolved UV photoemission data reveal the corresponding Fermi surface and its removal upon the Peierls transition. The CDW phase is stable to well above room temperature.