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math.AP2008
On universality of critical behaviour in Hamiltonian PDEs
Boris Dubrovin
Our main goal is the comparative study of singularities of solutions to the systems of first order quasilinear PDEs and their perturbations containing higher derivatives. The study…
math.AP2007
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{…