Abstract
In the present paper, we study the existence and bifurcation of nontrivial solutions of the nonlinear Schrodinger–Korteweg–de Vries (NLS–KdV) and Schrodinger–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 Schrodinger systems with cubic nonlinearity.
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