Abstract
In this chapter we consider what can happen when we try to compute a singular solution of the critical or supercritical NLS with a naive finite-difference scheme.
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Notes
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Nevertheless, this “mild” anisotropy can lead to multiple filamentation in NLS simulations (Sect. 25.2).
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To prove this inequality, simply consider separately the cases \(|\mathbf{w}| \le 1\) and \(|\mathbf{w}|> 1\).
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These discrete norms are the composite trapezoidal rules for \(\Vert \psi \Vert _2\).
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i.e., the numerical solution, computed with sufficiently refined grids in \(\mathbf{x}\) and \(z\).
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Fibich, G. (2015). Effects of Spatial Discretization. In: The Nonlinear Schrödinger Equation. Applied Mathematical Sciences, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-12748-4_30
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DOI: https://doi.org/10.1007/978-3-319-12748-4_30
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