Abstract
In this paper we study the smoothness properties of solutions to the KP-I equation. We show that the equation's dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data ϕ possesses certain regularity and sufficient decay as x → ∞ , then the solution u ( t ) will be smoother than ϕ for 0 < t ⩽ T where T is the existence time of the solution.
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