A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin–Ono and KdV equations are presented as well.

中文翻译：

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关于在电流存在下内部波的中间长波传播

研究了在中间长波近似情况下在电流存在下内部波的波动模型。下层要深得多，密度要比上层高。假定为近似平面。流体不可压缩且不粘稠。模型方程是在存在深度变化电流的情况下从动力学的哈密顿公式得出的。结果表明，适当的换算导致可积分的中长波方程（ILWE）。还介绍了导致可积本杰明-奥诺方程和KdV方程的ILWE的两个极限。