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Stationary problems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1756)

Abstract

As we have already noted in the Introduction, the substitution of the general representation for standing waves u(x, t) = e iwtφ(x), ω ∈ R, into the NLSE leads to the stationary equation

$$ \Delta \phi - \omega \phi + f(\phi ^2 )\phi = 0, x \in R^N , \phi = \phi (x). (II.0.1) $$
(II.0.1)

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Stationary problems. In: Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory. Lecture Notes in Mathematics, vol 1756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45276-1_4

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  • DOI: https://doi.org/10.1007/3-540-45276-1_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41833-7

  • Online ISBN: 978-3-540-45276-8

  • eBook Packages: Springer Book Archive