arXiv subjects

D. Grecu

Publications and source records attributed to D. Grecu.

8 recordsLinked to original sources

arXiv2006

Statistical Approach of Modulational Instability in the Class of Derivative Nonlinear Schroedinger Equations

The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is found. The modulational instability is associated with a positive imaginary part of the frequency. The integral equation is solved for different types of initial distributions (delta-function, Lorentzian) and the results are compared with those obtained using a deterministic approach. The differences between modulation instability of the normal NLS equation and derivative NLS equations is emphasized.

nlin.SI↗

arXiv2004

Localised and nonlocalised structures in nonlinear lattices with fermions

We discuss the quasiclassical approximation for the equations of motions of a nonlinear chain of phonons and electrons having phonon mediated hopping. Describing the phonons and electrons as even and odd grassmannian functions and using the continuum limit we show that the equations of motions lead to a Zakharov-like system for bosonic and fermionic fields. Localised and nonlocalised solutions are discussed using the Hirota bilinear formalism. Nonlocalised solutions turn out to appear naturally for any choice of wave parameters. The bosonic localised solution has a fermionic dressing while the fermionic one is an oscillatory localised field. They appear only if some constraints on the dispersion are imposed. In this case the density of fermions is a strongly localised travelling wave. Also it is shown that in the multiple scales approach the emergent equation is linear. Only for the resonant case we get a nonlinear fermionic Yajima-Oikawa system. Physical implications are discussed.

nlin.SI↗

arXiv2002

Statistical approach of the modulational instability of the discrete self-trapping equation

The discrete self-trapping equation (DST) represents an useful model for several properties of one-dimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view, considering the oscillator amplitude as a random variable. A kinetic equation for the two-point correlation function is written down, and its linear stability is studied. Both a Gaussian and a Lorentzian form for the initial unperturbed wave spectrum are discussed. Comparison with the continuum limit (NLS equation) is done.

nlin.SI↗

arXiv1999

Beyond Nonlinear Schrödinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interaction

Multi scales method is used to analyze a nonlinear differential-difference equation. In order $ε^3$ the NLS equation is found to determine the space-time evolution of the leading amplitude. In the next order this has to satisfy a complex mKdV equation (the next in the NLS hierarchy) in order to eliminate secular terms. The zero dispersion point case is also analyzed and the relevant equation is a modified NLS equation with a third order derivative term included

solv-int↗

arXiv1998

Long range interaction corrections on the quantum vibronic soliton

Self-localized modes in a quantum vibronic system, with long range interaction of Kac-Baker type and interacting nonlinearly with an acoustical phonon bath, is studied. One works in the coherent state approximation. Following a procedure of Sarker and Krumhansl, the problem is reduced to a nearest neighbours one. In the continuum limit the localized state satisfy a mKdV equation. An approximate expression for its frequency is found.

solv-int↗

arXiv1997

Continuum limit of nonlinear discrete systems with long range interaction potentials

One dimensional nonlinear lattices with harmonic long range interaction potentials (LRIP) having an inverse power kernel type, are studied. For the nearest neighbour nonlinear interaction we consider the anharmonic potential of the Fermi-Pasta-Ulam problem and the ϕ^3+ϕ^4 potential as well. The continuum limit is obtained following the method used by Ishimori and several Boussinesq and KdV type equations with supplementary Hilbert transform terms are found. These nonlocal terms are introduced by the LRIP. For the ϕ^3+ϕ^4 nearest neighbour interactions the continuum approximation turns out to admit exact bilinearization in Hirota formalism. Exact rational nonsingular solutions are found. The integrability of these nonlocal equations and the connection with perturbed KdV are also discussed.

solv-int↗

arXiv1996

On a class of rational and mixed soliton-rational solutions of Toda lattice

A class of rational solutions of Toda lattice satisfying certain Backlund transformations and a class of mixed rational-soliton solutions (quasisolitons) in wronskian formare obtained using the method of Ablowitz and Satsuma. Also an extended class of rational solutions are found using an appropriate recursion relation. They are also solutions of Boussinesq equation and it is conjectured that there is a larger class of common solutions of both equations.

solv-int↗

arXiv1993

On the Lattice Corrections to the Free Energy of Kink-Bearing Nonlinear One-Dimensional Scalar Systems

A ri proof of the effective potential (lattice corrections included) deduced by Trullinger and Sasaki is given. Using asymptotic methods from the theory of differential equations depending on a large parameter, the lattice corrections to the kink and kink-kink contributions to the free energy are calculated. The results are in complete agreement with a first order correction to the energy of the static kink.

cond-mat↗