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A symmetry test for quasilinear coupled systems

Please always quote using this URN: urn:nbn:de:0297-zib-3901
  • It is well known that the following class of systems of evolution equations \begin{eqnarray} \label{nsgen} \cases{ u_{t}=u_{xx}+F(u,v,u_x,v_x),\cr v_{t}=-v_{xx}+G(u,v,u_x,v_x),\cr} \end{eqnarray} is very rich in integrable cases. The complete classification problem is very difficult. Here we consider only the most interesting (from our opinion) subclass of systems (1). Namely, we consider equations linear in all derivatives of the form \begin{eqnarray} \label{kvazgen} \cases{ u_t = u_{xx} + A_{1}(u,v) u_x + A_{2}(u,v) v_x + A_{0}(u,v)\cr v_t = - v_{xx} + B_{1}(u,v) v_x + B_{2}(u,v) u_x + B_{0}(u,v). \cr} \end{eqnarray} without any restrictions on the functions $A_{i}(u,v), B_{i}(u,v)$.

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Metadaten
Author:Vladimir V. Sokolov, Thomas Wolf
Document Type:ZIB-Report
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS
35-XX PARTIAL DIFFERENTIAL EQUATIONS
Date of first Publication:1999/01/04
Series (Serial Number):ZIB-Report (SC-99-02)
ZIB-Reportnumber:SC-99-02
Published in:Appeared in: Inverse Problems 15 (1998) L5-L11
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