Simulation of internal solitary waves with negative polarity in slowly varying medium

We consider the propagation of an internal solitary wave over two different types of varying depth regions, i.e. a gentle monotonic bottom slope connecting two regions of constant depth in two-layer fluid flow and a smooth bump. Here, we let the depth of the upper layer is smaller than the lower layer such that an internal solitary wave of negative polarity is generated. The appropriate model for this problem is the variable-coefficient extended Korteweg-de Vries equation, which is then solved numerically using the method of lines. Our numerical results show different types of transformation of the internal solitary wave when it propagates over the varying depth region depending on the depth of the lower layer after the varying depth region including generation of solitary wavetrain, adiabatic and non-adiabatic transformation of the internal solitary wave.