THE ALMOST PERIODIC SOLUTIONS TO THE EQUATIONS OF THE KdV HIERARCHY


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Abstract

The Milne equation is used as the auxiliary equation instead of the usual Schrödinger equation, when the almost periodic solutions of the KdV hierarchy are looked for. Its almost periodic solution is found for the finite band (gap) potential and its time dependence is determined in the general case, provided the potential satisfies the KdV equations. Further investigated problems are: trace formulas and their applications, the Bloch functions, conserved quantities, the Poisson brackets and the Hamiltonian system.

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