Orbital stability of solitary waves of the coupled Klein-Gordon-Zakharov equations

This paper investigates the orbital stability of solitary waves for the coupled Klein-Gordon-Zakharov (KGZ) equations where 0. Firstly, we rewrite the coupled KGZ equations to obtain its Hamiltonian form. And then, we present a pair of sech-type solutions of the coupled KGZ equations. Because the abstract orbital stability theory presented by Grillakis, Shatah, and Strauss (1987) cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves for the coupled KGZ equations. In our work, =1,=0 are advisable. Hence, we can also obtain the orbital stability of solitary waves for the classical KGZ equations which was studied by Chen. Copyright (c) 2016 John Wiley & Sons, Ltd.