Orbital stability of standing waves for a system of nonlinear Schrödinger equations with three wave interaction

Abstract

Abstract. We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schrödinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a characterization of the standing waves solutions as minimizers of an energy functional subject to three independent L 2 mass constraints. As a consequence, we establish existence and orbital stability of solitary waves.

Variational problems associated with a system of nonlinear Schrödinger equations with three wave interaction

“…(1.1) Theorem 1.2 is also the generalization of the result of Ardila [2] to the higher dimensional case and to the model with potentials.…”

“…We also note that our strategy of the proof of Theorem 1.1 is different from the one in Ardila [2] even in the case N = 1. (see Bhattarai [3] for related results to other three component system.…”

“…In N = 1, 1 < p < 1 + 4/N and α > 0, Ardila [2] had proved the compactness of a minimizing sequence for I ∞ (γ, µ, s).…”

Existence and convergence results of meromorphic solutions to the equilibrium system with angular velocity

“…There is the potential of considering the linearization characteristics to be further developed for the system of equilibrium boundary value problems. Ardila [20] studied the existence and stability of standing waves solutions of a threecoupled nonlinear Schrödinger system related to the Raman amplification in a plasma. Hu and Yin [21] considered dynamics of the compressible Navier-Stokes equation in one spatial dimension for a viscous fluid with vanishing thermal conductivity.…”

“…Motivated and inspired by the references [18][19][20][21], in this paper we further consider the following universal equilibrium equations with nondifferentiable boundary conditions:…”