dorsal/arxiv
View SchemaThe Three-Wave Resonant Interaction: Deformation of the Plane-Wave Solutions and Darboux Transformations
| Authors | F. Guil, M. Mañas |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9601002 |
| URL | https://arxiv.org/abs/solv-int/9601002 |
Abstract
The plane wave solutions of the three-wave resonant interaction in the plane are considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space gives solutions of the three-wave resonant interaction that can be understood as a Darboux transformation of the plane wave solutions. The method is extended further to obtain general Darboux transformations: for any solution of the three-wave interaction problem and vector solutions of the corresponding Lax pair large families of new solutions, expressed in terms of Grammian type determinants of these vector solutions, are given.
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"abstract": "The plane wave solutions of the three-wave resonant interaction in the plane\nare considered. It is shown that rank-one constraints over the right\nderivatives of invertible operators on an arbitrary linear space gives\nsolutions of the three-wave resonant interaction that can be understood as a\nDarboux transformation of the plane wave solutions. The method is extended\nfurther to obtain general Darboux transformations: for any solution of the\nthree-wave interaction problem and vector solutions of the corresponding Lax\npair large families of new solutions, expressed in terms of Grammian type\ndeterminants of these vector solutions, are given.",
"arxiv_id": "solv-int/9601002",
"authors": [
"F. Guil",
"M. Ma\u00f1as"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "The Three-Wave Resonant Interaction: Deformation of the Plane-Wave Solutions and Darboux Transformations",
"url": "https://arxiv.org/abs/solv-int/9601002"
},
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