Existence and bifurcation of nontrivial solutions for the coupled nonlinear Schrödinger–Korteweg–de Vries system

被引：0
作者：
Qiuping Geng
Mian Liao
Jun Wang
Lu Xiao
机构：
[1] Jiangsu University,Faculty of Science
[2] Virginia Polytechnic Institute and State University,Bradley Department of Electric and Computer Engineering
[3] Jiangsu University,School of Management
来源：
Zeitschrift für angewandte Mathematik und Physik | 2020年 / 71卷
关键词：
Nonlinear Schrödinger–Korteweg–de Vries system; Positive solutions; Bifurcation theory; 35J61; 35J20; 35Q55; 49J40;
D O I：
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学科分类号：
摘要：
In the present paper, we study the existence and bifurcation of nontrivial solutions of the nonlinear Schrödinger–Korteweg–de Vries (NLS–KdV) and Schrödinger–Korteweg–de Vries–Korteweg–de Vries (NLS–KdV–KdV) systems which arise from fluid mechanics. On the one hand, for both the three-wave system and the two-wave system, the existence/nonexistence, continuous dependence and asymptotic behavior of positive ground state solutions are established. On the other hand, multiple positive solutions are found via a combination of Nehari manifold and bifurcation methods for the attractive interaction case, which has not been found for the conventional nonlinear Schrödinger systems with cubic nonlinearity.
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