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

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~$u_{yy}=u_z{u}_{xy}-u_y{u}_{xz}$; (2) the 3D rdDym equation $u_{ty}=u_x{u}_{xy}-u_y{u}_{xx}$; (3) The basic Veronese web equation $u_{ty}=u_t{u}_{xy}-u_y{u}_{tx}$; (4) Pavlov's equation $u_{yy}=u_{tx}+u_y{u}_{xx}-u_x{u}_{xy}$.

References in corpus (1)

• Linearly degenerate PDEs and quadratic line complexes

Cited by in corpus (4)

• Nonlocal symmetries of Lax integrable equations: a comparative study
• Integrability properties of some symmetry reductions
• 2D reductions of the equation $u_{yy}=u_{tx}+u_y{u}_{xx}-u_x{u}_{xy}$ and their nonlocal symmetries
• Reductions of the universal hierarchy and rdDym equations and their symmetry properties