On the support of solutions to the fifth-order Kadomtsev–Petviashvili II equation in three-dimensional space

ABSTRACT

Considered herein is the Cauchy problem associated with the fifth-order -dimensional Kadomtsev–Petviashvili II equation. It is proved that, if a sufficiently smooth solution to this problem is supported compactly at two different instants of time, then it vanishes identically.

Keywords:

• The fifth-order -dimensional Kadomtsev–Petviashvili II equation
• unique continuation property
• Carleman type estimates
• compact support

AMS Subject Classifications:

• 35B30
• 35G25

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Y. Fu is partially supported by the NSF-China [grant number 11471259], [grant number 11631007].