arXiv subjects

Anca Visinescu

Publications and source records attributed to Anca Visinescu.

7 recordsLinked to original sources

arXiv2011

Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach

Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions.

nlin.SI↗

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↗

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↗

arXiv2000

Multiscale Analysis of a Davydov Model with an Harmonic Long Range Interaction of Kac-Baker Type

The classical equation of motion of a Davydov model in a coherent state approximation is analyzed using the multiple scales method. An exponentially decaying long range interaction (Kac-Baker model) was included. In the first order, the dominant amplitude has to be a solution of the nonlinear Schroedinger equation (NLS). In the next order, the second amplitude satisfies an inhomogeneous linearized NLS equation, the inhomogeneous term depending only on the dominant amplitude. In order to eliminate possible secular behaviour the dominant amplitude has to satisfy also the next equation in the NLS hierarchy (a complex modified KdV equation). When the second order derivative of the dispersion relation vanishes, the scaling of the slow space variable has to be changed, and a generalized NLS equation with a third order derivative is found for the dominant amplitude. As the coefficient of the third derivative is small, a perturbational approach is used to discuss the equation. A complete solution is given when the dominant amplitude is the one-soliton solution of the NLS equation.

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↗

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↗