Miura transformation for the “good” Boussinesq equation
(2023) In Studies in Applied Mathematics- Abstract
It is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura-type transformation exists also for the “good” Boussinesq equation. This transformation maps solutions of a second-order equation to solutions of the fourth-order Boussinesq equation. Just like in the case of mKdV and KdV, the correspondence exists also at the level of the underlying Riemann–Hilbert problems and this is in fact how we construct the new transformation.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/86a9e993-060a-4879-b0bc-8bc5e03f5056
- author
- Charlier, C. LU and Lenells, J. LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- epub
- subject
- keywords
- Boussinesq equation, integrable system, Miura transformation, Riemann–Hilbert problem
- in
- Studies in Applied Mathematics
- publisher
- Wiley-Blackwell
- external identifiers
-
- scopus:85168155296
- ISSN
- 0022-2526
- DOI
- 10.1111/sapm.12631
- language
- English
- LU publication?
- yes
- id
- 86a9e993-060a-4879-b0bc-8bc5e03f5056
- date added to LUP
- 2023-11-13 13:27:18
- date last changed
- 2023-11-13 13:28:52
@article{86a9e993-060a-4879-b0bc-8bc5e03f5056,
abstract = {{<p>It is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura-type transformation exists also for the “good” Boussinesq equation. This transformation maps solutions of a second-order equation to solutions of the fourth-order Boussinesq equation. Just like in the case of mKdV and KdV, the correspondence exists also at the level of the underlying Riemann–Hilbert problems and this is in fact how we construct the new transformation.</p>}},
author = {{Charlier, C. and Lenells, J.}},
issn = {{0022-2526}},
keywords = {{Boussinesq equation; integrable system; Miura transformation; Riemann–Hilbert problem}},
language = {{eng}},
publisher = {{Wiley-Blackwell}},
series = {{Studies in Applied Mathematics}},
title = {{Miura transformation for the “good” Boussinesq equation}},
url = {{http://dx.doi.org/10.1111/sapm.12631}},
doi = {{10.1111/sapm.12631}},
year = {{2023}},
}