Singular solutions of the Liouville equation on an interval (Q580599)

Real singular solutions of the Liouville equation \(\phi_{tt}- \phi_{xx}+2 \exp \phi =0\) are investigated on the interval [0,L] with the Gervais-Neveu type boundary conditions \(\lim_{x\to 0,L}(\partial \phi (t,x)/\partial x)\exp [-\phi (t,x)]=2\epsilon_{0,L}\) where \(\epsilon_{0,L}=\pm 1\). The Hamiltonian description of this class of solutions is given. A reducibility to Hamiltonian systems with finite number of degrees of freedom is demonstrated. These systems are characterized by a triplet of the topological invariants (M,N,\(\sigma)\).