Carleman estimates and unique continuation property for the Kadomtsev–Petviashvili equations

Abstract

We study the unique continuation property for the generalized Kadomtsev–Petviashvili (KP) equations and its regularized version. We use Carleman estimates to prove that if the solution of the KP equations vanishes in an open subset, then this solution is identically equal to zero in the horizontal component of the open subset.

Keywords:

• KP equations
• BBM trick
• Carleman estimates
• unique continuation property
• Treves' inequality

AMS Subject Classifications::

• 35B60
• 35Q53

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Erratum

Acknowledgement

The author thanks L. Dupaigne for his interest and useful comments.