We conjecture an integrability and linearizability test for dispersive Z(2)-lattice equations by using a discrete multiscale analysis. The lowest order secularity conditions from the multiscale expansion give a partial differential equation of the form of a nonlinear Schrodinger (NLS) equation. If the starting lattice equation is integrable then the resulting NLS-type equation turns out to be integrable, while if the starting equation is linearizable we get a linear Schrodinger equation. On the other hand, if we start with a non-integrable lattice equation the resulting equation can be both integrable and non-integrable. This conjecture is confirmed by many examples.
Heredero RH, Levi D, Petrera M, & Scimiterna C (2008). Multiscale expansion on the lattice and integrability of partial difference equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 41(31) [10.1088/1751-8113/41/31/315208].
Titolo: | Multiscale expansion on the lattice and integrability of partial difference equations | |
Autori: | ||
Data di pubblicazione: | 2008 | |
Rivista: | ||
Citazione: | Heredero RH, Levi D, Petrera M, & Scimiterna C (2008). Multiscale expansion on the lattice and integrability of partial difference equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 41(31) [10.1088/1751-8113/41/31/315208]. | |
Abstract: | We conjecture an integrability and linearizability test for dispersive Z(2)-lattice equations by using a discrete multiscale analysis. The lowest order secularity conditions from the multiscale expansion give a partial differential equation of the form of a nonlinear Schrodinger (NLS) equation. If the starting lattice equation is integrable then the resulting NLS-type equation turns out to be integrable, while if the starting equation is linearizable we get a linear Schrodinger equation. On the other hand, if we start with a non-integrable lattice equation the resulting equation can be both integrable and non-integrable. This conjecture is confirmed by many examples. | |
Handle: | http://hdl.handle.net/11590/136940 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |