Remarks on the mass constraint for KP type equations

Abstract

For a rather general class of equations of Kadomtsev-Petviashvili (KP) type, we prove that the zero-mass (in $x$) constraint is satisfied at any non zero time even if it is not satisfied at initial time zero. Our results are based on a precise analysis of the fundamental solution of the linear part and its anti $x$-derivative.

References in corpus (2)

• Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
• Global well-posedness for the KP-I equation on the background of a non localized solution

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• Derivation of a viscous KP equation including surface tension, and related equations
• The Cauchy problem for the fractional Kadomtsev-Petviashvili equations
• Stability of the line soliton of the KP-II equation under periodic transverse perturbations
• Stability of line solitons for the KP-II equation in ${\mathbb{R}}^2$, II
• Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations