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Supersymmetric extension of the Korteweg–de Vries equation
Journal of Mathematical Physics, 1988It is shown that among a one-parameter family of supersymmetric extensions of the Korteweg–de Vries equation, there is a special system that has an infinite number of conservation laws, which can be formulated in the second Hamiltonian structure, and which has a nontrivial Lax representation. Its modified version is also discussed.
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Journal of Mathematical Physics, 2010The initial-boundary value problem for the Korteweg–de Vries equation posed on a finite interval of the spatial variable is considered. Using the method of simultaneous spectral analysis of the associated Lax pair, this problem is mapped into a Riemann–Hilbert problem formulated in the complex plane of the spectral parameter, but with explicit ...
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