Local solution for the Kadomtsev-Petviashvili equation with periodic conditions |
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| Authors: | Isaza J Pedro Mejía L Jorge Volker Stallbohm |
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| Institution: | (1) Department of Mathematics, University Nacional de Colombia, A.A. 3840 Medellín, Colombia;(2) Department of Mathematics, Universidad de Antioquia and Universidad Nacional de Colombia, A.A. 1226 Medellín, Colombia;(3) Department of Mathematics, Universidad Nacional de Colombia, A.A. 3840 Medellín, Colombia |
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| Abstract: | In this article we prove a local existence and uniqueness theorem for the Kadomtsev-Petviashvili Equation (u
t
+u
xxx
+uu
x
)
x
−u
yy
=0) in the Sobolev spaces of orders≥3, with initial values in the same spaces, and periodic boundary conditions. This theorem improves previous results based
upon the application of singular perturbation techniques. |
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| Keywords: | |
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