On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves

K. Andreiev; I. Egorova

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On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves

机译：带有逐步波的初始数据的Korteweg-de Vries方程的长时间渐近性

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We discuss an asymptotical behavior of the rarefaction wave for the KdV equation in the region behind the wave front. The first and the second terms of the asymptotical expansion for such a solution with respect to large time were derived without detailed analysis in [1]. In the present work, we correct the formula for the second term by investigating the corresponding parametrix problem. We also study an in uence of the resonance on the asymptotical behavior of the solution.

机译：对于波前后方区域中的KdV方程，我们讨论了稀疏波的渐近行为。在[1]中没有详细分析的情况下，得出了这种解决方案相对于大时间的渐近展开的第一和第二项。在本文中，我们将通过研究相应的参数问题来更正第二项的公式。我们还研究了共振对溶液渐近行为的影响。

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《Journal of Mathematical Physics, Analysis, Geometry》 |2017年第4期|共19页
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K. Andreiev; I. Egorova;
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中图分类高等数学;
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1. Long-time asymptotics for the Korteweg-de Vries equation with step-like initial data [J] . Egorova I., Gladka Z., Kotlyarov V., Nonlinearity . 2013,第7期

机译：具有逐步初始数据的Korteweg-de Vries方程的长期渐近性
2. On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data: I. Schwartz-type perturbations [J] . Iryna Egorova, Katrin Grunert, Gerald Teschl Nonlinearity . 2009,第6期

机译：具有阶跃有限间隙初始数据的Korteweg-de Vries方程的柯西问题：I. Schwartz型摄动
3. Riemann-Hilbert problem to the modified Korteveg-de Vries equation: Long-time dynamics of the steplike initial data [J] . Kotlyarov V, Minakov A Journal of Mathematical Physics . 2010,第9期

机译：修改后的Korteveg-de Vries方程的Riemann-Hilbert问题：阶梯状初始数据的长期动力学
4. New exact solutions for Korteweg-de Vries Burgers equation and Korteweg-de Vries equation [C] . 2011 International Conference on Management Science and Industrial Engineering . 2011

机译：Korteweg-de Vries Burgers方程和Korteweg-de Vries方程的新精确解
5. Long-time dynamics of Korteweg-de Vries solitary waves over a variable bottom. [D] . Dejak, Steven Ivan. 2006

机译：可变底部上Korteweg-de Vries孤波的长期动力学。
6. Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations [O] . S M Rayhanul Islam, Kamruzzaman Khan, M Ali Akbar -1

机译：非定常Korteweg-de Vries和时间正则化长波方程的精确解
7. 3 LONG-TIME ASYMPTOTICS FOR THE KORTEWEG–DE VRIES EQUATION WITH STEPLIKE INITIAL DATA [O] . Iryna Egorova, Zoya Gladka, Volodymyr Kotlyarov, 2016

机译：3具有sTEpLIKE初始数据的KORTEWEG-DE VRIEs方程的长期渐近线性
8. Variable Coefficient Korteweg-de Vries Equations and Travelling Waves in an Inhomogeneous Medium [R] . Baby, B. V. 1987

机译：非均匀介质中变系数Korteweg-de Vries方程和行波

On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves

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