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- W2022279944 abstract "New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u(n), n = 1, …, N are constructed via Zakharov and Manakov documentclass[12pt]{minimal}begin{document}$overline{partial }$end{document}∂¯-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u(n) and calculated by documentclass[12pt]{minimal}begin{document}$overline{partial }$end{document}∂¯-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u(n). It is shown that the sums documentclass[12pt]{minimal}begin{document}$u= u^{(k_1)}+ldots + u^{(k_m)}$end{document}u=u(k1)+...+u(km), 1 ⩽ k1 < k2 < … < km ⩽ N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics." @default.
- W2022279944 created "2016-06-24" @default.
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- W2022279944 date "2013-03-01" @default.
- W2022279944 modified "2023-10-18" @default.
- W2022279944 title "About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation" @default.
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- W2022279944 doi "https://doi.org/10.1063/1.4795132" @default.
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