Abstract
This chapter, which assumes localized solutions vanishing at infinity, deals with the Lagrangian and Hamiltonian structures of the NLS equation and with the derivation of conservation laws, some of them being related through the Noether theorem to invariance properties of the action (see, e.g., Rasmussen and Rypdal 1986 and, for a comprehensive discussion, Ginibre 1998, where a systematic approach is presented). The so-called variance identity, or virial theorem which together with the conservation of the Hamiltonian plays a central role in proving finite-time singularities for the elliptic NLS equation, is also derived.
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© 1999 Springer-Verlag New York, Inc.
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(1999). Structural Properties. In: Sulem, C., Sulem, PL. (eds) The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse. Applied Mathematical Sciences, vol 139. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22768-9_2
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DOI: https://doi.org/10.1007/978-0-387-22768-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98611-1
Online ISBN: 978-0-387-22768-9
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