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A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields (2006)
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BibTeX
@MISC{Manakov06ahierarchy,
author = {S. V. Manakov and P. M. Santini},
title = {A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields},
year = {2006}
}
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Abstract
We study a hierarchy of integrable partial differential equations in 2 + 1 dimensions arising from the commutation of 2- dimensional vector fields, and we construct the formal solution of the associated Cauchy problems using the Inverse Scattering Transform for one-parameter families of vector fields recently introduced in [1, 2]. Due to the ring property of the space of eigenfunctions, the inverse problem can be formulated in three distinguished 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. 1
Keyphrases
dimensional vector field integrable pdes vector field suitable analytic eigenfunctions inverse problem formal solution distinguished way jost eigenfunction integrable partial differential equation inverse scattering transform associated cauchy problem linear integral equation scalar nonlinear riemann problem one-parameter family
