Abstract
Recently, solitary waves characterized by a mutual locking of the fundamental and second harmonics in quadratically nonlinear media attracted a lot of attention [1]. The excitation of solitary waves, the evolution of unstable ones or numerical collision experiments with them reveal a prominent feature of the solutions under consideration. It turns out that persistent oscillations appear in many cases. They are practically undamped and may exhibit fairly large amplitudes. The extreme stability of the excited oscillations is astonishing for a nonintgrable system. This also is of great importance for future applications. Given a realistic experimental situation the second harmonic is excited via the fundamental wave only and strong oscillations cannot be avoided. Thus a stationary solitary wave with no oscillations seems to be more or less an exception.
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