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On the Hamiltonian formalism for Korteweg—de Vries type hierarchies

✍ Scribed by V. G. Mikhalev

Publisher
Springer US
Year
1992
Tongue
English
Weight
256 KB
Volume
26
Category
Article
ISSN
0016-2663

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Solutions of the Korteweg-de Vries hierarchy are discussed. It is shown that results by Wazwaz [Wazwaz AM. Multiple-soliton solutions of the perturbed KdV equation. Commun Nonlinear Sci Simul 2010;15(11):3270-73] are the well-known consequences of the full integrability for the Korteweg-de Vries hie

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We derive an improved fully explicit expression for the right -hand sides of the matrix KdV hierarchy using the relation to the heat kernel of the one -dimensional Schrödinger operator. Our method of "matrix elements" produces, moreover, an explicit expression for the powers of a Schrödinger-like d