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Formal analysis of the Cauchy problem for a system associated with the \((2+1)\)-dimensional Krichever-Novikov equation. (English) Zbl 0844.35111

Summary: The singularity manifold equation of the Kadomtsev-Petviashvili equation, the so-called Krichever-Novikov equation, has an exact linearization to an overdetermined system of partial differential equations in three independent variables. We study in detail the Cauchy problem for this system as an example for the use of the formal theory of differential equations. A general existence and uniqueness theorem is established. Formal theory is then contrasted with Janet-Riquier theory in the formulation of Reid. Finally, the implications of the results for the Krichever-Novikov equation are outlined.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C10 Series solutions to PDEs
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35N05 Overdetermined systems of PDEs with constant coefficients
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