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Stability of Solitons in the Parametrically Driven and Damped Nonlinear Schrödinger Equation in Arbitrary Dimension
We study the spectral stability of soliton solutions of the parametrically driven and damped nonlinear Schrödinger (PDDNLS) equation with power-law nonlinearity $|Ψ|^{2κ}Ψ$ in $N$ dimensions. We identify two families of stationary solutions, $Ψ_\pm$, whose existence is determined by two conditions:
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