Geodesic
A~hierarchy of integrable partial differential equations in $2{+}1$
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 147-156

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We introduce a hierarchy of integrable partial differential equations in $2+1$ dimensions arising from the commutation of one-parameter families of vector fields, and we construct the formal 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 Riemann problem for suitable analytic eigenfunctions.
Keywords: integrable system, inverse scattering transform, family of vector fields, nonlinear Riemann problem.
Mots-clés : inverse spectral transformation 
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     title = {A~hierarchy of integrable partial differential equations in $2{+}1$},
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S. V. Manakov; P. M. Santini. A~hierarchy of integrable partial differential equations in $2{+}1$. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 147-156. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a10/