International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 608612 | https://doi.org/10.1155/S0161171204312408

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, vol. 2004, Article ID 608612, 12 pages, 2004. https://doi.org/10.1155/S0161171204312408

On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension

Received30 Dec 2003

Abstract

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.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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