在文獻中孤立波指的是傳播中波形不變之局部擾動；但在先前研究中也發現，當波動系統較為複雜或受到干擾時，小振幅之週期波可能伴隨著孤立波出現。因此時主要波形仍為孤立波之型式，所以在文獻中稱這樣的波動為廣義孤立波。本文利用漸近方法將雙層流體系統的二維勢流模型簡化成干擾Korteweg-de Vries（KdV）方程式，並在簡化模型問題之基礎上探討雙層流體系統中廣義孤立波之傳播特性。

在本文中我們同時利用漸近與數值方法來計算廣義孤立波之波形與波尾振幅。由漸近解與數值解結果之比較發現，當深長比較小（ ）時數值解與漸近解就越吻合。同時，當固定深長比為 且深度比 遠離臨界深度比 時，漸近解析解和數值解計算結果相當吻合。可是當靠近深度比臨界值時，不僅我們先前所推導出的干擾KdV模型問題失效，在數值解方面也仍有困難待解決。

Solitary waves are locally confined disturbances that propagate without distortion in the wave systems when nonlinear and dispersive effects balance each other. However, results from previous studies show that, under structural perturbations solitary waves may develop oscillatory tails of small amplitude. Such weakly radiating solitary waves usually are referred to as generalized solitary waves in the literature. In this thesis, we consider a two-layer ideal fluid system where generalized solitary waves may arise. However, in order that further analytical and numerical studies can be carried out more efficiently, here we employ standard asymptotic techniques to reduce the full model to a perturbed Korteweg-de Vries (KdV) model problem.

In the perturbed KdV equation so derived, we relate the effects of higher-order dispersion and quadratic and cubic nonlinearites to the density ratio and depth ration of the fluid system. Then, in the long-wave limit, generalized solitary wave solutions are calculated using the techniques of exponential asymptotics. Furthermore, exact numerical solutions for waves of arbitrary length scale are also obtained by a spectral method. Generally speaking, the asymptotic results agree well with the numerical results even when the length scale of the wave disturbances becomes quite small. However, when the depth ratio of the fluid system is close to a critical value, the quadratic term in the perturbed KdV equation becomes small, thus invalidating our asymptotic theory. Unfortunately, the numerical method also becomes quite inefficient in such limit, so the dynamics of generalized solitary waves in such limit still is not well studied.

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