# Vojčák P. Some integrability properties of a (3+1)-dimensional integrable generalization of the dKP equation, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)

Speaker: Petr Vojčák

Title: Some integrability properties of a (3+1)-dimensional integrable generalization of the dKP equation

Abstract:
We present some integrabitity properties of the following system of PDE's

${\displaystyle q_{z}=2u_{z}+w_{x}+2ww_{z},}$
${\displaystyle v_{z}=2q_{x}-3u_{x}-2w_{y}+2wu_{z}-2ww_{x}+2uw_{z}}$
${\displaystyle u_{t}=vu_{z}+qu_{x}-uv_{z}-wv_{x}+v_{y},}$
${\displaystyle w_{t}=q_{y}-2v_{x}+4wu_{x}-wq_{x}+qw_{x}+vw_{z}-uq_{z},}$

which provides a (3+1)-dimensional integrable generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation [see A. Sergyeyev, A new class of (3+1)-dimensional integrable systems related to contact geometry, arXiv:1401.2122].