Zobrazit v EDS

Boussinesq's equation for water waves: the soliton resolution conjecture for Sector IV

Uloženo v:
Podrobná bibliografie
Název: Boussinesq's equation for water waves: the soliton resolution conjecture for Sector IV
Autoři: Charlier, Christophe, Lenells, Jonatan
Přispěvatelé: Lund University, Faculty of Science, Centre for Mathematical Sciences, Mathematics (Faculty of Sciences), Lunds universitet, Naturvetenskapliga fakulteten, Matematikcentrum, Matematik (naturvetenskapliga fakulteten), Originator
Zdroj: Advanced Nonlinear Studies. 25(1):106-151
Témata: Natural Sciences, Mathematical Sciences, Mathematical Analysis, Naturvetenskap, Matematik, Matematisk analys
Popis: We consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these sectors we gave an exact expression for the leading asymptotic term in the case when no solitons are present. In this paper, we derive an asymptotic formula in Sector IV, characterized by xt ∈ (√13, 1), in the case when solitons are present. In particular, our results provide an exact expression for the soliton-radiation interaction to leading order and a verification of the soliton resolution conjecture for the Boussinesq equation in Sector IV.
Přístupová URL adresa: https://doi.org/10.1515/ans-2023-0154
Databáze: SwePub
Popis
Abstrakt:We consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these sectors we gave an exact expression for the leading asymptotic term in the case when no solitons are present. In this paper, we derive an asymptotic formula in Sector IV, characterized by xt ∈ (√13, 1), in the case when solitons are present. In particular, our results provide an exact expression for the soliton-radiation interaction to leading order and a verification of the soliton resolution conjecture for the Boussinesq equation in Sector IV.
ISSN:15361365
DOI:10.1515/ans-2023-0154