Intermediate nonlinear Schrödinger equation for internal waves in a fluid of finite depth

A new evolution equation is derived by means of an asymptotic multi-scale technique for quasi-harmonic internal waves in a fluid of finite depth. This equation is shown to generalize the nonlinear Schrödinger equation which appears in the small-depth limit. Soliton solutions to the equation are found in an explicit form and describe the localized dips propagating along a modulationally stable wave background.