Solphys '97 ProceedingsIndex



Finite-dimensional Systems Integrable via Inverse Scattering

F. Pempinelli and M. Boiti

Dipartimento di Fisica dell'Università and Sezione INFN,
73100 Lecce, Italy



Abstract


The discrete spectral problem of Ablowitz-Ladik is considered in the case in which the potential has a finite support of length L. The spectral transform is explicitly computed and a recurrence relation on the length L for computing it in L algebraic step is given. This spectral transform can be used to generate via the scattering method a finite dimensional version of the dynamical systems associated to the Ablowitz--Ladik spectral problem. A special case is considered in which the potential is constraint to evolve in time on a semi-line. It is shown that the time evolution of the corresponding spectral data is given by a Riccati equation and that, consequently, the system is integrable. The truncated soliton, i.e. the potential obtained by putting to zero the one soliton outside an interval of length L is examined in detail. The sufficient and necessary condition for having a soliton contained in the truncated soliton solution is derived.


Document


Pempinelli.ps.gz


Contact information


F. Pempinelli and M. Boiti

Dipartimento di Fisica dell'Università and Sezione INFN, 73100 Lecce, Italy
E-mail: pempi@le.infn.it
Phone: +39 832 320450
Fax: +39 832 320505
Institution WWW address: http://www.fisica.unile.it



Solphys '97 ProceedingsIndex