Description of the n-Orthogonal Curvilinear Coordinate Systems and Hamiltonian Integrable Systems of Hydrodynamic Type . Part 1 . Integration of the Lamé Equations

@inproceedings{Zakharov2003DescriptionOT,
  title={Description of the n-Orthogonal Curvilinear Coordinate Systems and Hamiltonian Integrable Systems of Hydrodynamic Type . Part 1 . Integration of the Lam{\'e} Equations},
  author={Vladimir E. Zakharov},
  year={2003}
}
The classical problem of description of n-Orthogonal Curvilinear Coordinate System in flat Euclidean space is solved by the Inverse Scattering Method. The developed method allows to describe Hamiltonian and semi-Hamiltonian Integrable systems of Hydrodynamic type.