Quasiclassical quantization of the Boussinesq breather emerging from the  kink localized mode

[en] The breather solution found by M. Tajiri and Y. Murakami for the Boussinesq equation is studied analytically. The new parameterization of the solution is proposed, allowing us to find exactly the existence boundary of the Boussinesq breather and to show that such a nonlinear excitation emerges from the linear localized mode of the kink solution corresponding to a shock wave analog in a crystal. We explicitly find the first integrals, namely the energy and the field momentum, and faithfully construct the adiabatic invariant for the Boussinesq breather. As a result, we carry out the quasiclassical quantization of the nonlinear oscillating solution, obtaining its energy spectrum, i.e., the energy dependence on the momentum and the number of states, and reveal the Hamiltonian equations for this particle-like excitation.

Disciplines :

Physics

Author, co-author :

Bogdan, M. M. ^✱

CHARKINA, Oksana ^✱; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

^✱ These authors have contributed equally to this work.

External co-authors :

yes

Language :

English

Title :

Quasiclassical quantization of the Boussinesq breather emerging from the kink localized mode

Publication date :

June 2025

Journal title :

Low Temperature Physics

ISSN :

1063-777X

eISSN :

1090-6517

Publisher :

American Institute of Physics, United States - New York

Peer reviewed :

Peer Reviewed verified by ORBi

Focus Area :

Physics and Materials Science

FnR Project :

Grant No. 17568826 (ELE-MENT)

Commentary :

21 pages, 7 figures To be published in Low Temp. Phys. V.51, N.6, 2025

Available on ORBilu :

since 21 February 2025

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