The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.
Critical asymptotic behavior for the Korteweg-de Vries equation and in random matrix theory
Explicit solutions to the Korteweg-de Vries equation on the half line
The Burgers equations and the Born rule
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