Comments on Periodic Waves and Solitons
- 1 January 1984
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 32 (1-3) , 353-366
- https://doi.org/10.1093/imamat/32.1-3.353
Abstract
Elementary arguments are given for various results in wave propagation. The first part concerns the representation of periodic waves as sums of solitons. These are given for the Korteweg—deVries, various modified Korteweg—deVries and Boussinesq equations. The analogy with Parker's solution for Burgers' equation, which uses a sum of shocks, is noted. The second part provides elementary proofs for some of the existing results on multiphase solutions to the Korteweg—deVries and Sinh-Gordon equations.Keywords
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