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arXiv · 2011.13235

The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem

Anne Boutet de Monvel·Iryna Karpenko·Dmitry Shepelsky
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Abstract

This paper deals with the Cauchy problem for the modified Camassa-Holm (mCH) equation \begin{alignat*}{4} &m_t+\left((u^2-u_x^2)m\right)_x=0,&\quad&m:= u-u_{xx},&\quad&t>0,&\;&-\infty 0$), where the leading asymptotic term of the deviation of the solution from the background is nontrivial: this term is given by modulated (with parameters depending on $\frac{x}{t}$), decaying (as $t^{-1/2}$) trigonometric oscillations.

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Anne Boutet de Monvel, Iryna Karpenko, Dmitry Shepelsky. 2020-11-26. The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem. https://arxiv.org/abs/2011.13235

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