arXiv subjects

A. S. Cârstea

Publications and source records attributed to A. S. Cârstea.

4 recordsLinked to original sources

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 the dynamics of rational solutions for 1-D generalized Volterra system

The Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions using the "long wave" limit procedure of Ablowitz and Satsuma, and appropriate "gauge" transformations. Their properties are also discussed and it is shown that these solutions interact elastically with no phase shift.

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↗