ISSN:
1572-9036
Keywords:
35N05
;
35C10
;
35A07
;
Krichever-Novikov equation
;
Cauchy problem
;
existence and uniqueness theorem
;
formal theory
;
Janet-Riquier theory
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01064168
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