24 citations · 67 across the 9 of their papers we have counts for
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Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlevé-II equation
T. Grava, C. Klein
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscill…
On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the {\it tritronquée} solution to the Painlevé-I equation
B. Dubrovin, T. Grava, C. Klein
We argue that the critical behaviour near the point of ``gradient catastrophe" of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation $ iεψ_t +\frac{…
Reciprocal transformations and flat metrics on Hurwitz spaces
S. Abenda, T. Grava
We consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Ham…
Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
T. Grava, C. Klein
We study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions a…