  In this work, we consider the electromechanical density pulse as a coupled
solitary waves represented by a longitudinal compression wave and an
out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We
analyzed using, the variational approach, the characteristics of the coupled
solitary waves in the presence of damping within the framework of coupled
nonlinear Burger-Korteweg-de Vries-Benjamin-Bona-Mahony (BKdV-BBM) equation. It
is shown that, the inertia parameter increases the stability of coupled
solitary waves while the damping parameter decreases it. Moreover, the presence
of damping term induces a discontinuity of stable regions in the inertia-speed
parameter space, appearing in he form of an island of points. Bell shape and
solitary-shock like wave profiles were obtained by varying the propagation
speed and their linear stability spectrum computed. It is shown that bell shape
solitary wave exhibit bound state eigenvalue spectrum, therefore stable. On the
other hand, the solitary-shock like wave profiles exhibit unbound state
eigenvalue spectrum and are therefore generally unstable.
