Electron. J. Differential Equations, Vol. 2021 (2021), No. 72, pp. 1-13.

Existence and nonlinear stability of solitary wave solutions for coupled Schrodinger-KdV systems

Pengxue Cui, Shuguan Ji

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.
DOI: https://doi.org/10.58997/ejde.2021.72

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Pengxue Cui
School of Mathematics and Statistics and
Center for Mathematics and Interdisciplinary Sciences
Northeast Normal University
Changchun 130024, China
email: cuipx0205@vip.163.com
Shuguan Ji
School of Mathematics and Statistics and
Center for Mathematics and Interdisciplinary Sciences
Northeast Normal University
Changchun 130024, China
email: jisg100@nenu.edu.cn

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