Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice

doi:10.1088/1674-1056/abbbf3

中国物理B ›› 2021, Vol. 30 ›› Issue (2): 20502-0.doi: 10.1088/1674-1056/abbbf3

收稿日期:2020-07-18 修回日期:2020-09-11 接受日期:2020-09-28 出版日期:2021-01-18 发布日期:2021-01-18

Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice

Nkeh Oma Nfor^1,†, Serge Bruno Yamgoué¹, and Francois Marie Moukam Kakmeni²

1 Department of Physics, Higher Teacher Training College Bambili, The University of Bamenda, P. O. Box 39, Bambili-Cameroon; 2 Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P. O. Box 63 Buea-Cameroon

Received:2020-07-18 Revised:2020-09-11 Accepted:2020-09-28 Online:2021-01-18 Published:2021-01-18
Contact: ^†Corresponding author. E-mail: omnkeh@gmail.com

摘要/Abstract

Abstract: We consider the Hamiltonian of α, β-Fermi Pasta Ulam lattice and explore the Hamilton-Jacobi formalism to obtain the discrete equation of motion. By using the continuum limit approximations and incorporating some normalized parameters, the extended Korteweg-de Vries equation is obtained, with solutions that elucidate on the Fermi Pasta Ulam paradox. We further derive the nonlinear Schrödinger amplitude equation from the extended Korteweg-de Vries equation, by exploring the reductive perturbative technique. The dispersion and nonlinear coefficients of this amplitude equation are functions of the α and β parameters, with the β parameter playing a crucial role in the modulational instability analysis of the system. For β greater than or equal to zero, no modulational instability is observed and only dark solitons are identified in the lattice. However for β less than zero, bright solitons are traced in the lattice for some large values of the wavenumber. Results of numerical simulations of both the Korteweg-de Vries and nonlinear Schrödinger amplitude equations with periodic boundary conditions clearly show that the bright solitons conserve their amplitude and shape after collisions.

Key words: Fermi Pasta Ulam, paradox, bright, dark

中图分类号: (Solitons)

05.45.Yv

. [J]. 中国物理B, 2021, 30(2): 20502-0.

Nkeh Oma Nfor, Serge Bruno Yamgou, and Francois Marie Moukam Kakmeni. Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice[J]. Chin. Phys. B, 2021, 30(2): 20502-0.

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Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice

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