Quasiperiodic solutions of the Korteweg-de Vries equation

Physical premises for the appearance of quasiperiodic solutions of the Korteweg-de Vries (KdV) equation are considered. Such solutions appear near singularities of the KdV equation describing, for example, polarization waves in a ferroelectric substance featuring the first-order phase transition or in an electron beam-waveguide structure system. The presence of a singularity results in that the velocity of longwave perturbations in the system becomes imaginary, which corresponds to the wave propagation in the range of nontransparency. The second harmonic generation is related to modulation of the initial periodic solution at the second (lower) frequency. (C) 2002 MAIK "Nauka/Interperiodica".