| Abstract: |
| The standing wave solutions of a coupled nonlinear Schrodinger equations with quadratic nonlinearities from Raman amplification of laser beam in a plasma are considered. For both the original three-wave system and a reduced two-wave system, the existence/nonexistence, continuous dependence and asymptotic behavior of positive ground state solutions are established. In particular, multiple positive standing wave solutions are found via a combination of variational and bifurcation methods for the attractive interaction case, which has not been found for the conventional nonlinear Schrodinger systems with cubic nonlinearities. |
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