caa a22 4500 47707703X CHVBK 20180405111441.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF01064168 doi (NATIONALLICENCE)springer-10.1007/BF01064168 Formal analysis of the Cauchy problem for a system associated with the (2+1)-dimensional Krichever-Novikov equation [Elektronische Daten] [Werner Seiler, Peter Vassiliou, Colin Rogers] 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. Kluwer Academic Publishers, 1996 Krichever-Novikov equation nationallicence Cauchy problem nationallicence existence and uniqueness theorem nationallicence formal theory nationallicence Janet-Riquier theory nationallicence Seiler Werner Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, D-76128, Karlsruhe, Germany aut Vassiliou Peter Faculty of Information Science and Engineering, University of Canberra, 2616, Belconnen, ACT, Australia aut Rogers Colin School of Mathematics, University of New South Wales, 2052, Sydney, NSW, Australia aut Acta Applicandae Mathematica Kluwer Academic Publishers; gopher://gopher.wkap.nl 42/3(1996-03-01), 249-265 0167-8019 42:3<249 1996 42 10440 https://doi.org/10.1007/BF01064168 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01064168 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Seiler Werner Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, D-76128, Karlsruhe, Germany aut NATIONALLICENCE 700 1- Vassiliou Peter Faculty of Information Science and Engineering, University of Canberra, 2616, Belconnen, ACT, Australia aut NATIONALLICENCE 700 1- Rogers Colin School of Mathematics, University of New South Wales, 2052, Sydney, NSW, Australia aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers; gopher://gopher.wkap.nl 42/3(1996-03-01), 249-265 0167-8019 42:3<249 1996 42 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer