Metastability of solitary roll wave solutions of the St. Venant equations with viscosity

► Analytical/numerical solitary wave stability study in viscous St. Venant equations is carried out. ► The Melnikov integral instability condition is derived by lending instability “rule of thumb”. ► Homoclinic is observed with stable point spectrum and unstable essential spectrum. ► A mechanism is proposed by which persistence of unstable solitary waves occurs. ► Time evolution supports conclusions, giving possibility of nearby stable periodics.