This paper presents an analytical investigation of the propagation of internal solitary waves in the ocean of finite depth. Using the multi-scale analysis and reduced perturbation methods, the integro-differential equation is derived, which is called the intermediate long wave (ILW) equation and can describe the amplitude of internal solitary waves. It can reduce to the Benjamin–Ono equation in the deep-water limit, and to the KdV equation in the shallow-water limit. Little attention has been paid to the features of integro-differential equations, especially for their conservation laws. Here, based on Hirota bilinear method, Bcklund transformations in bilinear form of ILW equation are derived and infinite number of conservation laws are given. Finally, we analyze the fission phenomenon of internal solitary waves theoretically and verify it through numerical simulation. All of these have potential value for the further research on ocean internal solitary waves.

本文对有限深度海洋内部孤立波的传播进行了分析研究。使用多尺度分析和减少的摄动方法，推导了积分微分方程，该方程称为中间长波（ILW）方程，可以描述内部孤立波的幅度。它可以在深水极限处简化为Benjamin–Ono方程，而在浅水极限处可以简化为KdV方程。积分微分方程的特征很少被关注，尤其是它们的守恒定律。在此，基于Hirota双线性方法，导出了ILW方程的双线性形式的Bcklund变换，并给出了无穷多个守恒律。最后，我们从理论上分析了内部孤立波的裂变现象，并通过数值模拟对其进行了验证。所有这些对于进一步研究海洋内部孤立波具有潜在的价值。