Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations

Abstract EN

In this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations.

Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched.

Lastly, we show that this type of solution is orbitally stable by periodic perturbations of the same wavelength as the underlying wave.