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): Difference between revisions

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| abstract = We present some integrabitity properties of the following system of PDE's
| abstract = We present some integrabitity properties of the following system of PDE's


<math>\begin{eqnarray*}
<math>q_z = 2u_z+w_x+2ww_z,</math>
q_z &=& 2u_z+w_x+2ww_z,\\
 
v_z &=& 2q_x-3u_x-2w_y+2wu_z-2ww_x+2uw_z,t\\
<math>v_z = 2q_x-3u_x-2w_y+2wu_z-2ww_x+2uw_z,t</math>
u_t &=& vu_z+qu_x-uv_z-wv_x+v_y,\\
 
w_t &=& q_y-2v_x+4wu_x-wq_x+qw_x+vw_z-uq_z,
<math>u_t = vu_z+qu_x-uv_z-wv_x+v_y,</math>
\end{eqnarray*}</math>
 
<math>w_t = q_y-2v_x+4wu_x-wq_x+qw_x+vw_z-uq_z,</math>


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}}.
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}}.

Revision as of 09:35, 30 September 2015

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

qz=2uz+wx+2wwz,

vz=2qx−3ux−2wy+2wuz−2wwx+2uwz,t

ut=vuz+qux−uvz−wvx+vy,

wt=qy−2vx+4wux−wqx+qwx+vwz−uqz,

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.

A joint work with H. Baran and A. Sergyeyev.

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