Quasi-Periodic Waves and Quasi-Solitary Waves in Stratified Fluid of Slowly Varying Depth

The nonlinear waves in a stratifiiedfiuid of slowly varying depth are inrestigated in this paper. The model considered here consists of a two-layer incompressible constant-density inviscid fiuid confined by a slightly uneren bottom and a horizontal rigid vrall. The Korteweg-de Vries (KdV) eguation with varving coeffieients is derived with the aid of the reductive perturbation method. By using the method of multiple scales, the upproximate solutions of this eguation are obtained. It is found that the uneve nness of bottom may lead to the generation of so-called quasi-periodic waves quasi-solitary waves, whose periods propugation velocities and wave profiles vary slowly. The relations of the period of guasi-periodic waves and of the amplitude, propagation velocity of quasi-solitary waves varying with the depth of fluid are also presented. The models with two horizontal rigid walls or single-layer fluid can be regarded as particular cases of those in this paper.