Singular sector of the Kadomtsev–Petviashvili hierarchy, ∂̄ operators of nonzero index, and associated integrable systems | Zendy

B. G. Konopelchenko | Zendy; Luis Martı́nez Alonso | Zendy; Елена Медина | Zendy

Open Access

Singular sector of the Kadomtsev–Petviashvili hierarchy, ∂̄ operators of nonzero index, and associated integrable systems

Author(s) -

B. G. Konopelchenko,

Luis Martı́nez Alonso,

Елена Медина

Publication year - 2000

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.533148

Subject(s) - integrable system , mathematics , hierarchy , codimension , pure mathematics , index (typography) , kadomtsev–petviashvili equation , space (punctuation) , construct (python library) , mathematical analysis , algebra over a field , partial differential equation , computer science , operating system , world wide web , economics , burgers' equation , market economy , programming language

Integrable hierarchies associated with the singular sector of the Kadomtsev– Petviashvili (KP) hierarchy, or equivalently, with δ̅ operators of nonzero index are studied. They arise as the restriction of the standard KP hierarchy to submanifolds of finite codimension in the space of independent variables. For higher δ̅ index these hierarchies represent themselves as families of multidimensional equations with multidimensional constraints. The δ̅ -dressing method is used to construct these hierarchies. Hidden Korteweg–de Vries, Boussinesq, and hidden Gelfand–Dikii hierarchies are considered, too

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