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arXiv · 1407.0246

Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems

H. Baran·I. S. Krasil'shchik·O. I. Morozov·P. Vojčák
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Abstract

We present a complete description of $2$-dimensional equations that arise as symmetry reductions of fourf $3$-dimensional Lax-integrable equations: (1) the universal hierarchy equation~$u_{yy}=u_zu_{xy}-u_yu_{xz}$; (2) the 3D rdDym equation $u_{ty}=u_xu_{xy}-u_yu_{xx}$; (3) The basic Veronese web equation $u_{ty}=u_tu_{xy}-u_yu_{tx}$; (4) Pavlov's equation $u_{yy}=u_{tx}+u_yu_{xx}-u_xu_{xy}$.

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H. Baran, I. S. Krasil'shchik, O. I. Morozov, P. Vojčák. 2014-07-01. Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems. https://doi.org/10.1080/14029251.2014.975532

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