Geodesic
On the form of dispersive shock waves of the Korteweg–de Vries equation
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 12 (2016) no. 1, pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that the long-time behavior of solutions to the Korteweg–de Vries shock problem can be described as a slowly modulated one-gap solution in the dispersive shock region. The modulus of the elliptic function (i.e., the spectrum of the underlying Schrödinger operator) depends only on the size of the step of the initial data and on the direction, $\frac{x}{t}=$const, along which we determine the asymptotic behavior of the solution. In turn, the phase shift (i.e., the Dirichlet spectrum) in this elliptic function depends also on the scattering data, and is computed explicitly via the Jacobi inversion problem. 
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I. Egorova; Z. Gladka; G. Teschl. On the form of dispersive shock waves of the Korteweg–de Vries equation. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 12 (2016) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/JMAG_2016_12_1_a0/

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