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• W3157881570 abstract "There are two cases when the nonlinear Schrodinger equation (NLSE) with an external complex potential is well-known to support continuous families of localized stationary modes: the ${cal PT}$-symmetric potentials and the Wadati potentials. Recently Y. Kominis and coauthors [Chaos, Solitons and Fractals, 118, 222-233 (2019)] have suggested that the continuous families can be also found in complex potentials of the form $W(x)=W_{1}(x)+iCW_{1,x}(x)$, where $C$ is an arbitrary real and $W_1(x)$ is a real-valued and bounded differentiable function. Here we study in detail nonlinear stationary modes that emerge in complex potentials of this type (for brevity, we call them W-dW potentials). First, we assume that the potential is small and employ asymptotic methods to construct a family of nonlinear modes. Our asymptotic procedure stops at the terms of the $varepsilon^2$ order, where small $varepsilon$ characterizes amplitude of the potential. We therefore conjecture that no continuous families of authentic nonlinear modes exist in this case, but that satisfy the equation up to $varepsilon^2$-error can indeed be found in W-dW potentials. Second, we consider the particular case of a W-dW potential well of finite depth and support our hypothesis with qualitative and numerical arguments. Third, we simulate the nonlinear dynamics of found pseudo-modes and observe that, if the amplitude of W-dW potential is small, then the pseudo-modes are robust and display persistent oscillations around a certain position predicted by the asymptotic expansion. Finally, we study the authentic stationary modes which do not form a continuous family, but exist as isolated points. Numerical simulations reveal dynamical instability of these solutions." @default.
• W3157881570 created "2021-05-10" @default.
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• W3157881570 date "2021-04-24" @default.
• W3157881570 modified "2023-09-27" @default.
• W3157881570 title "On non-existence of continuous families of stationary nonlinear modes for a class of complex potentials" @default.
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