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].

Multiscale expansion on the lattice and integrability of partial difference equations

LEVI, Decio;
2008

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/136940
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