In this paper we establish local existence of solutions for a new model to describe the propagation of an internal wave propagating at the interface of two immiscible fluids with constant densities, contained at rest in a long channel with a horizontal rigid top and bottom. We also introduce a spectral-type numerical scheme to approximate the solutions of the corresponding Cauchy problem and perform a complete error analysis of the semidiscrete scheme.
Grajales, J. C. M. (2014). Existence and Numerical Approximation of Solutions of an Improved Internal Wave Model. Mathematical Modelling and Analysis, 19(3), 309-333. https://doi.org/10.3846/13926292.2014.924039
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