Orbital stability of periodic waves

In this paper, we deal with the existence and orbital stability of periodic waves for a large class of dispersive equations. We use the classical theory of orbital stability to propose a method of obtaining orbital stability that can be applied to classes of dispersive equations which include Korteweg–de Vries (KdV)-type equations and non-linear Schrödinger equations. An important feature of the method is that the sufficient conditions for stability can be checked numerically, so that method can be used in problems where the waves are not known explicitly. As applications we study the orbital stability of periodic waves of 3-KdV–de Vries and logarithmic Schrödinger equations.