宽度缓慢均匀变化水槽中的非传播表面孤波

NON-PROPAGATING SOLITARY SURFACE WAVE IN A CHANNEL WITH UNIFORMLY AND SLOWLY VARYING WIDTH

用多重尺度微扰理论导出了宽度均匀缓变水糟中非传播孤波所服从的非线性方程及其解析解。结果指出，孤波恒向宽度较窄的一端近加速移动。加速度正比于宽度的变化率．本文所用的方法原则上可以推广于其他均匀缓变波导中线性波和非线性波的理论研究。

The nonlinear equation governing the non-propagating solitary wave and its ana-lytical solution in a channel with uniformly and slowly varying width has been de-rived using the perturbation theory of multiple scales.The result obtained predictsthat the solitarv wave always moves towards the narrow end of the channel with anapproximately uniform acceleration which is proportional to the variation rate of thewidth.The method in the present paper can be extended in principle to the theore-tical investigation of other linear and nonlinear waves in a uniformly and slowly va-rying wave guide.