On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension
We present a method to construct inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension. The temporal component is the adjoint of the linearized equation and the spatial component is a partial differential equation with respect to the spatial variables....
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| Language: | English |
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Hindawi Limited
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204312408 |
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doaj-073f5bb9b5d84a47a14d363d238815732020-11-24T22:44:12ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004583117312810.1155/S0161171204312408On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimensionH. H. Chen0J. E. Lin1Department of Physics and Astronomy, University of Maryland, College Park 20742, MD, USADepartment of Mathematical Sciences, George Mason University, Fairfax 22030, VA, USAWe present a method to construct inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension. The temporal component is the adjoint of the linearized equation and the spatial component is a partial differential equation with respect to the spatial variables. Although this idea has been known for the one-spatial dimension for some time, it is the first time that this method is presented for the case of the higher-spatial dimension. We present this method in detail for the Veselov-Novikov equation and the Kadomtsev-Petviashvili equation.http://dx.doi.org/10.1155/S0161171204312408 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
H. H. Chen J. E. Lin |
| spellingShingle |
H. H. Chen J. E. Lin On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension International Journal of Mathematics and Mathematical Sciences |
| author_facet |
H. H. Chen J. E. Lin |
| author_sort |
H. H. Chen |
| title |
On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension |
| title_short |
On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension |
| title_full |
On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension |
| title_fullStr |
On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension |
| title_full_unstemmed |
On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension |
| title_sort |
on a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2004-01-01 |
| description |
We present a method to construct inverse scattering problems for
integrable nonlinear evolution equations in the two-spatial
dimension. The temporal component is the adjoint of the linearized
equation and the spatial component is a partial differential
equation with respect to the spatial variables. Although this idea
has been known for the one-spatial dimension for some time, it is
the first time that this method is presented for the case of the
higher-spatial dimension. We present this method in detail for
the Veselov-Novikov equation and the
Kadomtsev-Petviashvili equation. |
| url |
http://dx.doi.org/10.1155/S0161171204312408 |
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AT hhchen onadirectconstructionofinversescatteringproblemsforintegrablenonlinearevolutionequationsinthetwospatialdimension AT jelin onadirectconstructionofinversescatteringproblemsforintegrablenonlinearevolutionequationsinthetwospatialdimension |
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1725692307442761728 |