On the instability of solitary waves solutions of the generalized Benjamin equation. (Q1413003)

The author studies the instability of solitary-wave solutions for a nonlinear evolution equation which is known as the generalized Benjamin equation. The author first reviews results about local and global well-posedness of the initial value problem associated with the generalized Benjamin equation, and then establishes spatial and time decay of the solitary wave solutions. Finally, the author presents the stability theory for the generalized Benjamin equation, and develops instability results for some Korteweg-de Vries type equations without requiring spectral conditions.