Open AccessEquations of Lax type with several brackets
Author(s) -
Raúl Felipe,
Raúl Velásquez
Publication year - 2018
Publication title -
revista de ciencias (on line)/revista de ciencias
Language(s) - English
Resource type - Journals
eISSN - 2248-4000
pISSN - 0121-1935
DOI - 10.25100/rc.v19i2.6272
Subject(s) - hierarchy , mathematics , type (biology) , bilinear interpolation , algebra over a field , sequence (biology) , identity (music) , bilinear form , algebraic number , pure mathematics , algebraic equation , lax pair , mathematical analysis , integrable system , nonlinear system , physics , ecology , statistics , genetics , quantum mechanics , economics , acoustics , market economy , biology
In the present paper we introduce a new hierarchy, each equation of which is defined by several brackets of two pseudodifferential operators. We deal with some algebraic properties of these equations. In particular, we show that, as in the classic case, they are related to the presence of an infinite sequence of first integrals. A new version of the Zakharov-Shabat type equations is proved. Formal solutions of this hierarchy are constructed using a “several brackets bilinear identity”