Remarks on the mass constraint for KP type equations

TL;DR

This paper demonstrates that for a broad class of KP-type equations, the zero-mass constraint in x is preserved over time, even if not initially satisfied, through analysis of the fundamental solution.

Contribution

It establishes the invariance of the zero-mass constraint for KP-type equations at all non-zero times, expanding understanding of their solution properties.

Findings

Zero-mass constraint is preserved over time for KP-type equations.

The analysis is based on the fundamental solution and its anti-derivative.

Results hold for a general class of 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.