The KdV equation on a half-line

Details The KdV equation on a half-line The KdV equation on a half-line

1999-10-08

arxiv.org/abs/solv-int/9910002v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages. Some revisions are made and more detailes are worked out in comparison with the previous version (which was of 11 pa

Scientific paper

The initial boundary value problem on a half-line for the KdV equation with the boundary conditions $u|_{x=0}=a\leq0$, $u_{xx}|_{x=0}=3a^2$ is integrated by means of the inverse scattering method. In order to find the time evolution of the scattering matrix it turned out to be sufficient to solve the Riemann problem on a hyperelliptic curve of genus two, where the conjugation matrices are effectively defined by initial data.

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