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Reduction on the dressing chain of the Schrödinger operator. (English. Russian original) Zbl 0968.35101

Theor. Math. Phys. 123, No. 3, 768-775 (2000); translation from Teor. Mat. Fiz. 123, No. 3, 424-432 (2000).
Summary: We reduce the problem of constructing real finite-gap solutions of the focusing modified Korteweg-de Vries equation to the dressing chain of the Schrödinger operator. We show that the Schrödinger operator spectral curve corresponding to such a solution is real. We give some restrictions on the initial data for the chain that lead to such solutions. We also consider a soliton reduction. We obtain compact representations for the multisoliton and breather solutions of the modified Korteweg-de Vries equation; these representations can be useful in developing the perturbation theory for various applied problems.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
35Q55 NLS equations (nonlinear Schrödinger equations)
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References:

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