TEMPORAL EVOLUTIONS AND STATIONARY WAVES FOR PERTURBED KDV EQUATION WITH NONLOCAL TERM

Abstract

Initial value problems as well as stationary solitary and periodic waves are investigated for a perturbed KdV equation including the Hilbert transform; ut + uux + βuxxx + η(ℋux - uxx) = 0 (η > 0). Multi-hump stationary solitary and periodic wave solutions are numerically identified. Furthermore, the close relation between the structure of the stationary waves and the behavior of the temporal evolutions is discussed in comparison with other perturbed KdV equations with different instability and dissipation terms. The results support some general features common to this type of nonlinear evolution equations.