Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 72, pp. 1-13.

Title: Existence and nonlinear stability of solitary wave solutions for 
       coupled Schrodinger-KdV systems
       
Authors: Pengxue Cui (Northeast Normal Univ., Changchun, China)
         Shuguan Ji  (Northeast Normal Univ., Changchun, China)

Abstract:
In this article, we consider the existence and nonlinear stability of the solitary wave
solutions to the coupled Schrodinger-KdV system. By using the undetermined coefficient method,
we construct the exact solitary wave solutions. Furthermore, we prove the nonlinear
stability of such solitary wave solutions with respect to small perturbations by
applying the classical stability theory developed by Benjamin [8] and Bona [9],
and the spectral analysis method.

Submitted March 2, 2021. Published September 10, 2021.
Math Subject Classifications: 35Q55, 35Q53, 35B35.
Key Words: Schrodinger-KdV system; nonlinear stability; solitary wave solution.