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Some Properties of Solutions to the Camassa–Holm-Type Equation with Higher-Order Nonlinearities

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Abstract

In this paper, we focus on the large time behavior of compact support of the potential for a Camassa–Holm-type equation with nonlinearities of degree \(k+1\) if the compactly supported initial potential keeps its sign. Moreover, persistence property in weighted Sobolev spaces is also investigated.

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Notes

  1. Private discussion with Professor Tudor Stefan Ratiu.

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Acknowledgements

The authors thank Professor Tudor Stefan Ratiu for his fruitful discussions and are very grateful to the anonymous reviewers for their careful reading and useful suggestions which greatly improved the presentation of the paper. This work was partially supported by National Natural Science Foundation of China, under Grant No. 11301394 and China Postdoctoral Science Foundation, under Grant No. 2017M620149.

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Correspondence to Zhengguang Guo.

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Communicated by Melvin Leok.

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Guo, Z., Li, X. & Yu, C. Some Properties of Solutions to the Camassa–Holm-Type Equation with Higher-Order Nonlinearities. J Nonlinear Sci 28, 1901–1914 (2018). https://doi.org/10.1007/s00332-018-9469-7

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  • DOI: https://doi.org/10.1007/s00332-018-9469-7

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