Dan Grecu

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A system of coupled NLS equations (integrable and non-integrable) is discussed using a Madelung fluid description. The problem is equivalent with a two-component fluid of densities ρ 1 and ρ 2 and velocities υ 1 and υ 2 , which satisfy equations of continuity and equations of motion. Provided that the nonlinear coupling coefficients are identical, several(More)
The modulational instability (MI) of some discrete nonlinear evolution equations, representing approximations of Davydov's model of α-helix in protein, is studied. In a multiple scales analysis the dominant amplitude usually satisfies the nonlinear Schrödinger equation (NLS), or the Zakharov–Benney equations (ZB), if a long wave-short wave resonance takes(More)
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(More)
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 nonlin-ear Schrödinger equation (NLS). In the next order the second(More)
Multi scales method is used to analyze a nonlinear differential-difference equation. In the order ǫ 3 the NLS eq. is found to determine the space-time evolution of the leading amplitude. In the next order this has to satisfy a complex mKdV eq. (the next in the NLS hierarchy) in order to eliminate secular terms. The zero dispersion point case is also(More)
One-dimensional nonlinear lattices with harmonic long range interaction potentials (LRIP) of inverse power type are studied. For the nearest neighbour nonlinear interaction we shall consider the anharmonic potential of the Fermi-Pasta-Ulam problem and the φ 3 +φ 4 as well. The continuum limit is obtained following the method used by Ishimori [1], and(More)
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(More)
A spherically symmetric model for a non-necrotic vascularized tumor, proposed several years ago by Byrne and Chaplain (1995) [9], was reviewed and extended. The nutrient and inhibitor concentrations are satisfying reaction-diffusion equations, and the tumor radius is determined from a very simple integro-differential equation obtained from the balance of(More)
W ith the Internet's rise to prominence, we're moving to a new understanding of the nature of computation. 1 From the times of Leibniz and Babbage until the late 1950s, computation was understood as calculation, or the manipulation of numbers. Throughout the next decade (and still perhaps for many people), computation came to be understood as information(More)