Abstract
In Chap. 1 we saw that propagation of linearly-polarized paraxial cw laser beams in a bulk Kerr medium is modeled by the two-dimensional cubic NLS. In this chapter we show that the one-dimensional and three-dimensional cubic NLS also arise in physical models.
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Notes
- 1.
i.e., the solution \(\tilde{\psi }(z,x,y)\) of (4.1) with \(\tilde{\psi }_0(x,y) = \psi _0(x)(1+ \epsilon g(x,y))\) should remain close to \(\psi (z,x)\) for any \(g(x,y)\) and \(\epsilon \ll 1\).
- 2.
- 3.
See, e.g., [10] for analysis of dimension reduction in the GP/NLS equation.
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© 2015 Springer International Publishing Switzerland
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Fibich, G. (2015). NLS Models. In: The Nonlinear Schrödinger Equation. Applied Mathematical Sciences, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-12748-4_4
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DOI: https://doi.org/10.1007/978-3-319-12748-4_4
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