Aspects of Integrability in One and Several Dimensions,
CLARKSON UNIV POTSDAM NY
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The results on Inverse Scattering in multidimensions and on the algebraic properties of equations in 21 i.e. two spatial and one temporal dimensions should be of particular interest With respect to algebraic properties of equations in 21, the question of finding the recursion operator and the bi-Hamiltonian formulation of these equations has remained open for a rather long time. It was even doubted in the literature if the relevant results in 11 could be extended to 21. It was recently shown that equations in 21 solvable via the Inverse Scattering Transform are bi-Hamiltonian systems. Also given are the recursion and bi-Hamiltonian operators for large classes of equations in 21, including the Kadomtsev-Petviashvili a two dimensional analogue of the Korteweg-deVries and the Davey-Stewartson a two dimensional analogue of the nonlinear Schrodinger equations.
- Numerical Mathematics