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The “good” Boussinesq
equation: long-time asymptotics
Christophe Charlier, Jonatan Lenells and Deng-Shan Wang |
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Vol. 16 (2023), No. 6, 1351–1388
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Abstract |
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We consider the initial-value problem for the “good” Boussinesq equation on the line. Using inverse scattering techniques, the solution can be expressed in terms of the solution of a -matrix Riemann–Hilbert problem. We establish formulas for the long-time asymptotics of the solution by performing a Deift–Zhou steepest descent analysis of a regularized version of this Riemann–Hilbert problem. Our results are valid for generic solitonless Schwartz class solutions whose space-average remains bounded as . |
Keywords
asymptotics, Boussinesq equation, Riemann–Hilbert problem,
inverse scattering transform, initial value problem
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Mathematical Subject Classification
Primary: 34E05, 35G25, 35Q15, 37K15, 76B15
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Milestones
Received: 19 June 2020
Revised: 2 November 2021
Accepted: 20 December 2021
Published: 23 August 2023
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Authors |
| Christophe Charlier | |
| Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden |
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| Jonatan Lenells | |
| Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden |
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| Deng-Shan Wang | |
| Laboratory of Mathematics and
Complex Systems School of Mathematical Sciences Beijing Normal University Beijing China |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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