Solitary Waves in a Two-Layer Fluid with Piecewise Exponential Stratification

The problem of internal stationary waves in a two-layer fluid with a density, which exponentially depends on the depth inside the layers and undergoes a jump at the interface, is considered. A nonlinear equation is derived in the second-order long-wave approximation, and asymptotic submodels describing solitary waves of finite amplitude are examined. The dispersion properties and wave-propagation modes depending on the dimensionless parameters of the background piecewise constant flow are studied.