A Derivation of Conserved Quantities and Symmetries for the Multi-Dimensional Soliton Equations
Since the study on the KdV equation by Miura[l], it has been shown that soliton equations have the remarkable properties, the existence of an infinite number of conserved quantities and symmetries. Several methods have been proposed successfully to show these properties for the equations which have one spatial dimension. However, for the higher dimensional cases or for the discrete equations, the problems are rather complicated and it is not so easy to give the explicit expressions.
KeywordsLinear Problem Nonlinear Evolution Equation Nonlinear Partial Differential Equation Toda Lattice High Dimensional Case
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- M. Sato and Y. Sato, in Nonlinear Partial Differential Equations in Applied Science, ed. by H. Fujita, P. D. Lax and G. Strang (Kinokuniya/North Holland, Tokyo, 1983) 259.Google Scholar
- E. Date, M. Jimbo, M. Kashiwara and T. Miwa, in Non-linear integrable Systems-Classical Theory and Quantum Theory, ed. M. Jimbo and T. Miwa (World Scientific, Singapore, 1983) 39.Google Scholar
- K. Ueno and K. Takasaki, in Group Representation and Systems of Differential Equations, Adv. Stud, in Pure Math. 4(Kinokuniya, Tokyo, 1984) 1.Google Scholar
- K. Kajiwara and J. Satsuma, to appear in J. Math. Phys.Google Scholar