Model equation of the theory of solitons |
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Authors: | V É Adler A B Shabat |
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Institution: | (1) Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia |
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Abstract: | We consider the hierarchy of integrable (1+2)-dimensional equations related to the Lie algebra of vector fields on the line.
We construct solutions in quadratures that contain n arbitrary functions of a single argument. A simple equation for the generating
function of the hierarchy, which determines the dynamics in negative times and finds applications to second-order spectral
problems, is of main interest. Considering its polynomial solutions under the condition that the corresponding potential is
regular allows developing a rather general theory of integrable (1+1)-dimensional equations.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 29–45, October, 2007. |
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Keywords: | hierarchy of commuting vector fields Riemann invariant Dubrovin equations |
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