Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Nonlinear surface waves on a tangential discontinuity in magnetohydrodynamics


Authors: Giuseppe Alì and John K. Hunter
Journal: Quart. Appl. Math. 61 (2003), 451-474
MSC: Primary 35L60; Secondary 76W05
DOI: https://doi.org/10.1090/qam/1999831
MathSciNet review: MR1999831
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Abstract: We derive an asymptotic equation that describes the propagation of weakly nonlinear surface waves on a tangential discontinuity in incompressible magnetohydrodynamics. The equation is similar to, but simpler than, previously derived asymptotic equations for weakly nonlinear Rayleigh waves in elasticity, and is identical to a model equation for nonlinear Rayleigh waves proposed by Hamilton et al. The most interesting feature of the surface waves is that their nonlinear self-interaction is nonlocal. As a result of this nonlocal nonlinearity, smooth solutions break down in finite time, and appear to form cusps.


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DOI: https://doi.org/10.1090/qam/1999831
Article copyright: © Copyright 2003 American Mathematical Society

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