Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra

Iryna Egorova; Johanna Michor; Gerald Teschl

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Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra

机译：Toda冲击问题的长期渐近性：非重叠谱

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We derive the long-time asymptotics for the Toda shock problem usingthe nonlinear steepest descent analysis for oscillatory Riemann{Hilbert factorizationproblems. We show that the half-plane of space/time variablessplits into ve main regions: The two regions far outside where the solutionis close to the free backgrounds. The middle region, where the solution canbe asymptotically described by a two band solution, and two regions separatingthem, where the solution is asymptotically given by a slowly modulatedtwo band solution. In particular, the form of this solution in the separatingregions veri es a conjecture from Venakides, Deift, and Oba from 1991.

机译：我们通过使用非线性最陡下降分析来分析振荡Riemann {Hilbert因式分解问题，从而得出了Toda冲击问题的长期渐近性。我们表明，时空变量的半平面分为五个主要区域：远离解决方案的自由区域附近的两个区域。中间区域，其中的解可以由两频带解渐近地描述，而两个区域将它们分开，其中区域由缓慢调制的两频带解渐近地给出。特别是，该解决方案在分离区域中的形式来自1991年的Venakides，Deift和Oba的猜想。

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《Journal of Mathematical Physics, Analysis, Geometry》 |2018年第4期|共46页
作者
Iryna Egorova; Johanna Michor; Gerald Teschl;
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中图分类高等数学;
关键词
Toda latticeRiemann{Hilbert problemshock wave;

机译：Toda格子Riemann {希尔伯特问题冲击波;

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1. Long-time asymptotics of the periodic Toda lattice under short-range perturbations [J] . Kamvissis S., Teschl G. Journal of Mathematical Physics . 2012,第7期

机译：短时扰动下周期性Toda格的长期渐近性
2. LONG-TIME ASYMPTOTICS OF THE TODA LATTICE FOR DECAYING INITIAL DATA REVISITED [J] . Kruger H, Teschl G Reviews in mathematical physics . 2009,第1期

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3. Long-time asymptotics for the Toda lattice in the soliton region [J] . Helge Krüger, Gerald Teschl Mathematische Zeitschrift . 2009,第3期

机译：孤子区中Toda晶格的长期渐近性
4. Long-Time Asymptotics for the Buckley-Leverett Models of Development of Oil and Gas Fields [C] . Atlas V. Akhmetzyanov, Alexei G. Kushner, Valentin V. Lychagin IEEE International Conference on Application of Information and Communication Technologies . 2017

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5. Long-time asymptotics of the nonlinear Schroedinger equation shock problem. [D] . Buckingham, Robert John. 2005

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6. Universal Regimes in Long-Time Asymptotic of Multilevel Quantum System Under Time-Dependent Perturbation [O] . Vladimir Akulin 2021

机译：在时间依赖性扰动下多级量子系统长期渐近的普遍制度
7. Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra [O] . Egorova, Iryna, Michor, Johanna, Teschl, Gerald 2014

机译：Toda冲击问题的长时渐近性：非重叠光谱
8. Long-Time Asymptotics of a System for Plasma Diffusion [R] . Rosenau, P., Turkel, E. 1985

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Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra

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