In this paper, we revisit the well-posedness for the Benney-Roskes system (also known as Zakharov-Rubenchik systems) for N = 1, 2, 3, and establish the nonlinear orbital stability of ground state standing waves in the case N = 1, by using the variational approach induced by the Hamiltonian structure and the Liapunov method.
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Jose Raul Quintero Henao (2024) studied this question.
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