Existence and stability of solitary waves for the generalized Korteweg-de Vries equations
Existence and stability of solitary waves for the generalized Korteweg-de Vries equations
In this paper, we consider the fractional Korteweg-de Vries equations with general nonlinearities. By studying constrained minimization problems and applying the method of concentration-compactness, we obtain the existence of solitary waves for the generalized Korteweg-de Vries equations under some assumptions of the nonlinear term. Moreover, we prove that the set …