  We apply the version of the method of simplest equation called modified
method of simplest equation for obtaining exact traveling wave solutions of a
class of equations that contain as particular case a nonlinear PDE that models
shallow water waves in viscous fluid (Topper-Kawahara equation). As simplest
equation we use a version of the Riccati equation. We obtain two exact
traveling wave solutions of equations from the studied class of equations and
discuss the question of imposing boundary conditions on one of these solutions.
