LieCanonicalForm

\documentstyle[11pt]{article}
\input{latlib}
\parindent 0mm
\begin{document}

\centerline{\fbox{\parbox{8cm}{\Large\bf UserFunction LieCanonicalForm} }}

\vspace*{3mm}
\vspace*{1mm}\noindent{\bf LieCanonicalForm}$(u:ODE)$

The single argument $u$ may be second- or third-order quasilinear differential equation. Its  coefficients are rational functions in the independent variable and may contain in addition one or more parameters.

The function {\em LieCanonicalForm} returns the symmetry class of $u$ and the canonical form corresponding to it.

\vspace*{1mm}\noindent{\bf Related Functions:} {\em SymmetryClass(u:ODE)}.

\vspace*{1mm}\noindent{\bf Examples.} The input is given in {\em Reduce} algebraic mode syntax. The output for each minisession is returned in a separate window.

\5{\tt depend y,x;}

\5{\tt LieCanonicalForm }

\vspace*{1mm}\hspace*{30mm}
\fbox{
 \begin{displaymath}
 \begin{array}{l}
  {\rm The\1 differential\1 equation:}\\[2mm]
  x y''y'-y''y-y'^2-2y'-1 = 0\\[2mm]
  {\rm Symmetry Class:}\2 {\cal S}^2_{2,1}\\[2mm]
  {\rm The Canonical Form:}\\[1mm]
  {v''}+\fracsm{{v'}^{3}-3{v'}^{2}+{v'}}{{v'}-1}=0
 \end{array}
 \end{displaymath} }


\vspace*{5mm}

{\bf References}

S.~Lie, {\em Vorlesungen \"{u}ber Differentialgleichungen mit bekannten infinitesimalen Transformationen}, Teubner, Leipzig, 1981 [Reprinted by Chelsea Publishing Company, New York, 1967].

 


\end{document}

 

User Interface Functions

Go back to parent