Integration of the mKdV hierarchy with integral type of source

Details Integration of the mKdV hierarchy with integral type of source Integration of the mKdV hierarchy with integral type of source

2002-05-13

arxiv.org/abs/nlin/0205024v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, Latex, to be published in Journal of Physics A

Scientific paper

We investigate the mKdV hierarchy with integral type of source (mKdVHWS), which consist of the reduced AKNS eigenvalue problem with $r=q$ and the mKdV hierarchy with extra term of the integration of square eigenfunction. First we propose a method to find the explicit evolution equation for eigenfunction of the auxiliary linear problems of the mKdVHWS. Then we determine the evolution equations of scattering data corresponding to the mKdVHWS which allow us to solve the equation in the mKdVHWS by inverse scattering transformation.

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