Special Issue: Dedicated to the Memory of Frank Olver (Part I)No Access

On the blow-up of solutions to the integrable modified Camassa–Holm equation

Yue Liu

Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China

Department of Mathematics, University of Texas, Arlington, TX 76019, USA

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Peter J. Olver

School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

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Changzheng Qu

Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China

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, and

Shuanghu Zhang

Department of Mathematics, Southwest University, Chongqing 400715, P. R. China

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https://doi.org/10.1142/S0219530514500274Cited by:50 (Source: Crossref)

Abstract

We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the modified integrable Camassa–Holm equation with cubic nonlinearity. The blow-up conditions are formulated in terms of the initial momentum density and the average initial energy.

Dedicated to Frank W. J. Olver, in remembrance of his many fundamental contributions to mathematics and science.

Keywords:

AMSC: 35B44, 35G25

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