Periodic and conditionally periodic analogs of the many-soliton solutions of the Korteweg-de Vries equation
نویسندگان
چکیده
A method of connecting the Korteweg~e Vries (KdV) equation, known from the theory of nonlinear waves, with the SchrOdinger equation was discovered in 1967,Pl This method is applied in the present paper to a study of a periodic problem. We find exact analytical formulae for a class of solutions u (x ,t) such that at any moment in time t the potential u (x ,t) of the Schrodinger operator has only a ftnite number of forbidden bands in the Bloch spectrum. We ftnd in this connection all potentials with a ftnite number of bands. This class of solutions contains as a degenerate limiting case the well known N-soliton solutions of the KdV equation, which decrease
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