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Chin. Phys. B, 2021, Vol. 30(2): 020502    DOI: 10.1088/1674-1056/abbbf3
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Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice

Nkeh Oma Nfor1,†, 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
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.
Keywords:  Fermi Pasta Ulam      paradox      bright      dark  
Received:  18 July 2020      Revised:  11 September 2020      Accepted manuscript online:  28 September 2020
PACS:  05.45.Yv (Solitons)  
Corresponding Authors:  Corresponding author. E-mail: omnkeh@gmail.com   

Cite this article: 

Nkeh Oma Nfor, Serge Bruno Yamgou, and Francois Marie Moukam Kakmeni Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice 2021 Chin. Phys. B 30 020502

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