STABILITY AND INSTABILITY OF SOLITARY WAVE SOLUTIONS OF A NONLINEAR DISPERSIVE SYSTEM OF BENJAMIN-BONA-MAHONY TYPE ∗ Sevdzhan Hakkaev

This paper concerns the orbital stability and instability of soli- tary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the soli- tary waves.