TITLE:
Existence for a Higher Order Coupled System of Korteweg-de Vries Equations
AUTHORS:
Min Liu
KEYWORDS:
System of Korteweg-de Vries Equations, Normalized Vector Solitary Waves, Variation Approach
JOURNAL NAME:
Applied Mathematics,
Vol.12 No.4,
April
19,
2021
ABSTRACT: Consider the following system of coupled Korteweg-de Vries equations, where u, v⊆ W2,2, 2≤N≤7and λi,β > 0, β denotes a real coupling parameter. Firstly, we prove the existence of the solutions of a coupled system of Korteweg-de Vries equations using variation approach and minimization techniques on Nehari manifold. Then, we show the multiplicity of the equations by a bifurcation theory which is rare for studying higher order equations.