Rigorous asymptotics of a KdV soliton gas

Autor:	Girotti, Manuela, Grava, Tamara, Jenkins, Robert, McLaughlin, Ken D. T. -R.
Rok vydání:	2018
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs Nonlinear Sciences - Pattern Formation and Solitons Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-021-03942-1
Popis:	We 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 $N\to \infty$ of a gas of $N$-solitons. We show that this gas of solitons in the limit $N \to \infty$ is slowly approaching a cnoidal wave solution for $x \to - \infty$ (up to terms of order $\mathcal{O} (1/x)$), while approaching zero exponentially fast for $x\to+\infty$. 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. Comment: 42 pages, 7 figures. To appear in Comm. Math. Physics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1807.00608 Zobrazit plný text záznamu View this record from Arxiv