Abstract
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.
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Seiler, W.M., Vassiliou, P.J. & Rogers, C. Formal analysis of the Cauchy problem for a system associated with the (2+1)-dimensional Krichever-Novikov equation. Acta Appl Math 42, 249–265 (1996). https://doi.org/10.1007/BF01064168
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DOI: https://doi.org/10.1007/BF01064168