dorsal/arxiv
View SchemaComplete integrability of a modified vector derivative nonlinear Schroedinger equation
| Authors | Ralph Willox, Willy Hereman, Frank Verheest |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9407002 |
| URL | https://arxiv.org/abs/solv-int/9407002 |
| DOI | 10.1088/0031-8949/52/1/003 |
Abstract
Oblique propagation of magnetohydrodynamic waves in warm plasmas is described by a modified vector derivative nonlinear Schroedinger equation, if charge separation in Poisson's equation and the displacement current in Ampere's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schroedinger 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 Schroedinger equation, the recursion operator for the latter one is now readily available.
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"abstract": "Oblique propagation of magnetohydrodynamic waves in warm plasmas is described\nby a modified vector derivative nonlinear Schroedinger equation, if charge\nseparation in Poisson\u0027s equation and the displacement current in Ampere\u0027s law\nare properly taken into account. This modified equation cannot be reduced to\nthe standard derivative nonlinear Schroedinger equation and hence its possible\nintegrability and related properties need to be established afresh. Indeed, the\nnew equation is shown to be integrable by the existence of a bi--Hamiltonian\nstructure, which yields the recursion operator needed to generate an infinite\nsequence of conserved densities. Some of these have been found explicitly by\nsymbolic computations based on the symmetry properties of the new equation.\nSince the new equation includes as a special case the derivative nonlinear\nSchroedinger equation, the recursion operator for the latter one is now readily\navailable.",
"arxiv_id": "solv-int/9407002",
"authors": [
"Ralph Willox",
"Willy Hereman",
"Frank Verheest"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0031-8949/52/1/003",
"title": "Complete integrability of a modified vector derivative nonlinear Schroedinger equation",
"url": "https://arxiv.org/abs/solv-int/9407002"
},
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