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- W1661863042 abstract "Taking the Korteweg-de Vries equation as an example of a soliton system, a connection between conservation laws and infinitesimal transformations (symmetries) is investigated. It is shown that there exist an infinite number of form-invariant infinitesimal transformations. A one-to-one correspondence between conservation laws and infinitesimal transformations is established explicitly. Then it is concluded that the Korteweg-de Vries equation has an infinite number of conservation laws, each of which corresponds to the symmetry of the system. Two methods of weaving an infinitesimal transformation into a finite one are presented; one of them is the extension of the Lie transformation to the nonlinear case, and the other is a transformation reducible to the Backlund transformation. Furthermore, it is found that Hamiltonian formalism naturally leads to the quantization of the wave field. During the discussions, a number of conjectures and theorems which have been proposed in earlier works are confirmed by using the infinitesimal transformation extensively." @default.
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- W1661863042 date "1978-10-01" @default.
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- W1661863042 title "Invariances and Conservation Laws of the Korteweg-de Vries Equation" @default.
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- W1661863042 doi "https://doi.org/10.1002/sapm1978592153" @default.
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