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Creators/Authors contains: "Rybkin, Alexei"

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  1. (, Nonlinearity)
    Abstract We put forward a new approach to Deift-Trubowitz type trace formulas for the 1D Schrodinger operator with potentials that are summable with the first moment (short-range potentials). We prove that these formulas are preserved under the KdV flow whereas the class of short-range potentials is not. Finally, we show that our formulas are well-suited to study the dispersive smoothing effect. 
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  2. ; ; ; ; ; (, Journal of Ocean Engineering and Marine Energy)
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  3. ; ; (, Applied Mathematics Letters)
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  4. (, Communications in Mathematical Physics)
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  5. (, Studies in Applied Mathematics)
    Abstract In the Korteweg–de Vries equation (KdV) context, we put forward a continuous version of the binary Darboux transformation (aka the double commutation method). Our approach is based on the Riemann–Hilbert problem and yields a new explicit formula for perturbation of the negative spectrum of a wide class of step‐type potentials without changing the rest of the scattering data. This extends the previously known formulas for inserting/removing finitely many bound states to arbitrary sets of negative spectrum of arbitrary nature. In the KdV context, our method offers same benefits as the classical binary Darboux transformation does. 
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  6. ; (, Nonlinearity)
    Abstract In the context of the Cauchy problem for the Korteweg–de Vries equation we extend the inverse scattering transform to initial data that behave at plus infinity like a sum of Wigner–von Neumann type potentials with small coupling constants. Our arguments are based on the theory of Hankel operators. 
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  7. ; ; ; (, Pure and Applied Geophysics)
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  8. ; ; ; ; (, SoftwareX)
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  9. (, Nonlinearity)
    null (Ed.)
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  10. (, Studies in Applied Mathematics)
    Abstract In the KdV context, we revisit the classical Darboux transformation in the framework of the vector Riemann–Hilbert problem. This readily yields a version of the binary Darboux transformation providing a short‐cut to explicit formulas for solitons traveling on a wide range of background solutions. Our approach also links the binary Darboux transformation and the double commutation method. 
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