We introduce a hierarchy of integrable partial differential equations in 2+1 dimensions arising from the commutation of one-para,meter families of vector fields, and we construct the lormal solution of the associated Cauchy problems using the inverse scattering method for one-parameter families of vector fields. Because the space of eigenfunctions is a ring, the inverse problem can be formulated in three distinct ways. In particular, one formulation corresponds to a linear integral equation for a Jost eigenfunction, and another formulation is a scalar nonlinear niemann problein for suitable analytic eigenlunctions.

A hierarchy of integrable partial differential equations in 2+1 dimensions associated with one-parameter families of one-dimensional vector fields / S. V., Manakov; Santini, Paolo Maria. - In: THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 0040-5779. - STAMPA. - 152:1(2007), pp. 1004-1011. ((Intervento presentato al convegno 4th Workshop on Nonlinear Physics - Theory and Experiment IV tenutosi a Gallipoli, ITALY nel JUN 22-JUL 01, 2006 [10.1007/s11232-007-0084-2].

### A hierarchy of integrable partial differential equations in 2+1 dimensions associated with one-parameter families of one-dimensional vector fields

#### Abstract

We introduce a hierarchy of integrable partial differential equations in 2+1 dimensions arising from the commutation of one-para,meter families of vector fields, and we construct the lormal solution of the associated Cauchy problems using the inverse scattering method for one-parameter families of vector fields. Because the space of eigenfunctions is a ring, the inverse problem can be formulated in three distinct ways. In particular, one formulation corresponds to a linear integral equation for a Jost eigenfunction, and another formulation is a scalar nonlinear niemann problein for suitable analytic eigenlunctions.
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family of vector fields; integrable system; inverse scattering transform; inverse spectral transformation; nonlinear riemann problem
01 Pubblicazione su rivista::01a Articolo in rivista
A hierarchy of integrable partial differential equations in 2+1 dimensions associated with one-parameter families of one-dimensional vector fields / S. V., Manakov; Santini, Paolo Maria. - In: THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 0040-5779. - STAMPA. - 152:1(2007), pp. 1004-1011. ((Intervento presentato al convegno 4th Workshop on Nonlinear Physics - Theory and Experiment IV tenutosi a Gallipoli, ITALY nel JUN 22-JUL 01, 2006 [10.1007/s11232-007-0084-2].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/84837`
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