Two-component Camassa-Holm system and its reductions
Duration: 60 mins
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About this item
| Description: |
Matsuno, Y
Wednesday 9th August 2017 - 11:30 to 12:30 |
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| Created: | 2017-08-10 13:21 |
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| Collection: | Nonlinear Water Waves |
| Publisher: | Isaac Newton Institute |
| Copyright: | Matsuno, Y |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | My talk is mainly concerned with an integrable two-component Camassa-Holm (CH2) system which describes the propagation of nonlinear shallow water waves. After a brief review of strongly nonlinear models for shallow water waves including the Green-Naghdi and related systems, I develop a systematic procedure for constructing soliton solutions of the CH2 system. Specifically, using a direct method combined with a reciprocal transformation, I obtain the parametric representation of the multisoliton solutions, and investigate their properties. Subsequently, I show that the CH2 system reduces to the CH equation and the two-component Hunter-Saxton (HS2) system by means of appropriate limiting procedures. The corresponding expressions of the multisoliton solutions are presented in parametric forms, reproducing the existing results for the reduced equations. Also, I discuss the reduction from the HS2 system to the HS equation. Last, I comment on an interesting issue associated with peaked wave (or peakon) solutions of the CH, Degasperis-Procesi, Novikov and modified CH equations. |
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