On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension
نویسندگان
چکیده
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 higherspatial dimension. We present this method in detail for the Veselov-Novikov equation and the Kadomtsev-Petviashvili equation.
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عنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2004 شماره
صفحات -
تاریخ انتشار 2004