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• W1990289434 abstract "It has been known for some time that solitons of the externally driven, damped nonlinear Schrödinger equation can only exist if the driver’s strength, h, exceeds approximately (2/π)γ, where γ is the dissipation coefficient. Although this perturbative result was expected to be correct only to the leading order in γ, recent studies have demonstrated that the formula hthr=(2/π)γ gives a remarkably accurate description of the soliton’s existence threshold prompting suggestions that it is, in fact, exact. In this note we evaluate the next order in the expansion of hthr(γ) showing that the actual reason for this phenomenon is simply that the next-order coefficient is anomalously small: hthr=(2/π)γ+0.002γ3. Our approach is based on a singular perturbation expansion of the soliton near the turning point; it allows to evaluate hthr(γ) to all orders in γ and can be easily reformulated for other perturbed soliton equations." @default.
• W1990289434 created "2016-06-24" @default.
• W1990289434 creator A5018186937 @default.
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• W1990289434 date "1999-08-01" @default.
• W1990289434 modified "2023-09-26" @default.
• W1990289434 title "Existence threshold for the ac-driven damped nonlinear Schrödinger solitons" @default.
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• W1990289434 doi "https://doi.org/10.1016/s0167-2789(99)00055-x" @default.
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