ASYMPTOTIC SOLUTIONS OF THE NON-LINEAR WAVE EQUATION OF VAN-DER-POL TYPE ON THE INFINITE LINE*
DOI:
https://doi.org/10.4314/njt.71.368Abstract
Using multiple time and spatial scales it is shown that for the wave equation with a small Van-der-Pol nonlinearity on the infinite line, initially oscillatory waves (with or without slowly-varying amplitudes) leading to saw-tooth waves. If the initial conditions are localised, non- oscillatory, and decay fast enough to zero at infinity then the leading asymptotically valid solution becomes unbounded at large times. But if the initial disturbance vanishes outside a finite interval the leading approximation approaches finite saw-tooth waves at large times.Downloads
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