These are the state variables, time/space flux functions and the dimension of the system

Out[39]=

{u, v}

Out[40]=

{u, v}

Out[41]=

{P[v], -u}

Out[42]=

2

Time-Flux-matrix, Space-Flux-matrix:

Out[49]//MatrixForm=

( 1 0 ) 0 1

Out[50]//MatrixForm=

( ′ ) 0 P [v] -1 0

This is the quasi-linear flux matrix:

Out[53]//MatrixForm=

( ′ ) 0 P [v] -1 0

Eigenvalues, Right Eigenvectors, Left Eigenvectors:

Out[58]//MatrixForm=

( ′ ) - Sqrt[P [v]] ′  Sqrt[P [v]]

Out[59]//MatrixForm=

( ′ ′ )  Sqrt[P [v]] - Sqrt[P [v]] 1 1

Out[60]//MatrixForm=

(  ) -------------------- ... ------------------- 1 ′ - 2 Sqrt[P [v]] 2

Lie Bracket Matrix, Lie Bracket Coefficient Matrix

Out[68]//MatrixForm=

( ( ′̸ ... ( 0 ) 0 0

Out[69]//MatrixForm=

( ( ′′ ) &# ... ) ′ 2 P [v] 0

Tensor of interaction coefficients

Out[72]//MatrixForm=

( ( ′′ ) &# ... ′ 2 P [v] 0

Created by Mathematica  (October 15, 2004)