Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions

Chen, Wenxiong; Li, Congming; Li, Guanfeng

doi:10.48550/arxiv.1604.04806

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Symmetry Of Solitary Waves1

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Cited by 2 publications

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“…Since the nonlocal operator H c of the steady Whitham equation corresponds to an inhomogeneous kernel function a Kelvin-type transform is not appropriate in our case. It is worth mentioning that in [10,11] the authors generalize the result in [12] and establish maximum principles for a class of nonlocal equations which originate from the fractional Laplace operators.…”

Section: Symmetry Of Solitary Wavesmentioning

confidence: 85%

Symmetry and decay of traveling wave solutions to the Whitham equation

Bruell¹,

Ehrnström²,

Pei³

2017

Journal of Differential Equations

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This paper is concerned with decay and symmetry properties of solitary wave solutions to a nonlocal shallow water wave model. It is shown that all supercritical solitary wave solutions are symmetric and monotone on either side of the crest. The proof is based on a priori decay estimates and the method of moving planes. Furthermore, a close relation between symmetric and traveling wave solutions is established

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Section: Symmetry Of Solitary Wavesmentioning

confidence: 85%