Unified approach to action-angle representation of real and complex multisolitons

Oevel, Gudrun; Fuchssteiner, Benno

doi:10.1016/0378-4371(92)90094-7

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…In the present paper we show that the MVDNLS possesses a bi-Hamiltonian structure, and hence through the resulting recursion operator an infinite sequence of conserved densities. Interestingly enough, to the best of our knowledge there seems to be no proof in the literature that the DNLS itself has a bi-Hamiltonian structure, although this expected property is mentioned sometimes without further details nor references (Oevel and Fuchssteiner 1992). The existence of an infinite sequence of conserved densities is proved by Kaup and Newell (1978) for the DNLS, without showing the bi-Hamiltonian character.…”

Section: Introductionmentioning

confidence: 97%

The Nonlinear Schrödinger Equation

Ferreira¹

2011

Nonlinear Effects in Optical Fibers

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Oblique propagation of magnetohydrodynamic waves in warm plasmas is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation and hence its possible integrability and related properties need to be established afresh. Indeed, the new equation is shown to be integrable by the existence of a bi-Hamiltonian structure, which yields the recursion operator needed to generate an infinite sequence of conserved densities. Some of these have been found explicitly by symbolic computations based on the symmetry properties of the new equation. Since the new equation includes as a special case the derivative nonlinear Schrödinger equation, the recursion operator for the latter one is now readily available.

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Section: Introductionmentioning

confidence: 97%

The Nonlinear Schrödinger Equation

Ferreira¹

2011

Nonlinear Effects in Optical Fibers

View full text Add to dashboard Cite

show abstract

“…Interestingly enough, to the best of our knowledge there seems to be no proof in the literature that the DNLS itself has a bi-Hamiltonian structure, although this expected property is mentioned sometimes without further details nor references (Oevel and Fuchssteiner 1992). The existence of an infinite sequence of conserved densities is proved by Kaup and Newell (1978) for the DNLS, without showing the bi-Hamiltonian character.…”

Section: Introductionmentioning

confidence: 99%