Author:
Girotti M.,Grava T.,Jenkins R.,McLaughlin K. D. T.-R.
Abstract
AbstractWe analytically study the long time and large space asymptotics of a new broad class of solutions of the KdV equation introduced by Dyachenko, Zakharov, and Zakharov. These solutions are characterized by a Riemann–Hilbert problem which we show arises as the limit $$N\rightarrow + \infty $$
N
→
+
∞
of a gas of N-solitons. We show that this gas of solitons in the limit $$N\rightarrow \infty $$
N
→
∞
is slowly approaching a cnoidal wave solution for $$x \rightarrow - \infty $$
x
→
-
∞
up to terms of order $$\mathcal {O} (1/x)$$
O
(
1
/
x
)
, while approaching zero exponentially fast for $$x\rightarrow +\infty $$
x
→
+
∞
. We establish an asymptotic description of the gas of solitons for large times that is valid over the entire spatial domain, in terms of Jacobi elliptic functions.
Funder
H2020 European Research Council
Directorate for Mathematical and Physical Sciences
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
13 articles.
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