This paper is concerned with the orbital stability for solitary waves of a system of coupled KdV-equations. Although the coupled equations are not in Hamiltonian form, we can apply the abstract results of Grillakis et al. [4, 5] and use a detailed spectral analysis to obtain the stability of the solitary waves.
"Orbital stability of solitary waves of coupled KdV equations." Differential Integral Equations 12 (3) 295 - 308, 1999. https://doi.org/10.57262/die/1367265213