The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles

Sergei M. Grudsky, Christian Remling, Alexei Rybkin

Type: Article

Publication Date: 2015-09-01

Citations: 8

DOI: https://doi.org/10.1063/1.4930001

Abstract

We develop the inverse scattering transform for the Korteweg-de Vries equation with real singular initial data q x of the form q x = r ′ x + r x 2 ⁠, where r ∈ L loc 2 ⁠, r|ℝ+ = 0. As a consequence, we show that the solution q x , t is a meromorphic function with no real poles for any t > 0.

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Journal of Mathematical Physics - View - PDF
arXiv (Cornell University) - View - PDF
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