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The Cauchy Problem for the Kadomtsev-Petviashvili (KPII) Equation in Three Space Dimensions |
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| Authors: | Pedro Isaza J Juan C López C Jorge Mejía L |
| Institution: | 1. Escuela de Matemáticas , Universidad Nacional de Colombia , Medellín, Colombia pisaza@unalmed.edu.co;3. Escuela de Matemáticas , Universidad Nacional de Colombia , Medellín, Colombia;4. Departamento de Matemáticas , Universidad de Pamplona , Pamplona, Colombia;5. Escuela de Matemáticas , Universidad Nacional de Colombia , Medellín, Colombia |
| Abstract: | We prove the existence and uniqueness of local solutions in time for the Kadomtsev-Petviashvili equation (KPII) in ?3 for initial data in a suitable anisotropic Sobolev space of functions which have essentially 1+ derivative in the variable x and 0+ derivatives in the variables y and z. |
| Keywords: | Local solutions Nonlinear dispersive equations |