Stability of Periodic Travelling Wave Solutions to the Kawahara Equation

摘要: We analyse the stability of periodic, travelling-wave solutions to Kawahara equation and some its generalizations. determine parameter regime for which these can exhibit resonance. By examining perturbations small-amplitude solutions, we show that generalised resonance is a mechanism high-frequency instabilities. derive quadratic fully determines region solutions. Focussing on obtain asymptotic results how their instabilities develop grow. Numerical computation used confirm illustrate regimes where our analysis does not apply.