Stability of traveling wave solutions for the second-order Camassa–Holm equation.

This paper studies the stability of traveling wave solutions of the second-order Camassa–Holm equation. Applying the pseudo-conformal transformation, the solutions near the travelling wave solutions of the second-order C–H equation are decomposed: λ 1 2 t u t , y + x t = η t , y + Q y . The uniform boundedness of the difference term is proved by smoothing technique, and the orbital stability of the traveling wave solution of the second-order C–H equation is obtained. [ABSTRACT FROM AUTHOR]