On the compatibility of overdetermined systems of double waves (Q1577391)

Let \(u:G\subseteq{\mathbb{R}}^n\rightarrow{\mathbb{R}}^m\) be a smooth enough mapping; let \(A_\alpha(u)\), \(\alpha\in\{1,\ldots,n\}\), be an \(N\times m\) matrix depending on \(u\); let \(f(u)\) be an \(N\)-vector-function also depending on \(u\). Assume that \(u\) is a solution of the system \[ \sum^n_{\alpha=1}A_\alpha(u)\displaystyle\;\frac{\partial u}{\partial x_\alpha}=f(u). \] \noindent \(u\) is called a multiple wave of rank \(r\), where is the rank of its Jacobi matrix. Thus a ``double wave'' means a multiple wave of rank \(r=2\). The article presents the classification of irreducible double waves with \(N=2n-1\).