arXiv:1210.7434v2 [nlin.SI] 10 Jun 2013 Page 1 arXiv:1210.7434v2 [nlin.SI] 10 Jun 2013
LONG-TIME ASYMPTOTICS FOR THE KORTEWEG–DE VRIES EQUATION WITH STEPLIKE …

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of
the Korteweg–de Vries equation with steplike initial data leading to a rarefaction wave. In …

We study the determinant\det (I-γ K_s), 0< γ< 1 det (I-γ K s), 0< γ< 1, of the integrable
Fredholm operator K s acting on the interval (− 1, 1) with kernel K_s (λ, μ)=\sin s (λ-μ) π (λ-μ) …

Using the matrix Riemann--Hilbert factorization approach for nonlinear evolution systems
which take the form of Lax-pair isospectral deformations and whose corresponding Lax …

Soliton theory and the theory of Hankel (and Toeplitz) operators have stayed essentially
hermetic to each other. This paper is concerned with linking these two very active and …

On the KdV equation with steplike finite-gap initial data Page 1 Nonlinearity On the Cauchy
problem for the Korteweg–de Vries equation with steplike finite-gap initial data: I. Schwartz-type …

Given a suitable solution V (t, x) to the Korteweg–de Vries equation on the real line, we
prove global well-posedness for initial data u (0, x)∈ V (0, x)+ H-1 (R). Our conditions on V …

1 Introduction Page 1 ON THE CAUCHY PROBLEM FOR THE KORTEWEGDE VRIES
EQUATION WITH STEPLIKE FINITE-GAP INITIAL DATA II. PERTURBATIONS WITH FINITE …

KdV on an incoming tide Page 1 Nonlinearity PAPER KdV on an incoming tide To cite this
article: Thierry Laurens 2022 Nonlinearity 35 343 View the article online for updates and …

We are concerned with the Cauchy problem for the KdV equation on the whole line with an
initial profile V 0 which is decaying sufficiently fast at+∞ and arbitrarily enough (ie no decay …