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Journal article
Generalized solitary waves in the gravity‐capillary Whitham equation
Studies in applied mathematics (Cambridge), v 144(1)
Jan 2020
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Abstract
We study the existence of traveling wave solutions to a unidirectional shallow water model, which incorporates the full linear dispersion relation for both gravitational and capillary restoring forces. Using functional analytic techniques, we show that for small surface tension (corresponding to Bond numbers between 0 and 1/3) there exists small amplitude solitary waves that decay to asymptotically small periodic waves at spatial infinity. The size of the oscillations in the far field are shown to be small beyond all algebraic orders in the amplitude of the wave.
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Details
- Title
- Generalized solitary waves in the gravity‐capillary Whitham equation
- Creators
- Mathew A. Johnson - University of KansasJ. Douglas Wright - Drexel University
- Publication Details
- Studies in applied mathematics (Cambridge), v 144(1)
- Publisher
- Wiley
- Number of pages
- 29
- Grant note
- National Science Foundation (DMS‐1511488; DMS‐1614785)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000494188500001
- Scopus ID
- 2-s2.0-85074559835
- Other Identifier
- 991019182775904721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied