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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 |
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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.
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Received: 18 July 2020
Revised: 11 September 2020
Accepted manuscript online: 28 September 2020
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PACS:
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05.45.Yv
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(Solitons)
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Corresponding Authors:
†Corresponding author. E-mail: omnkeh@gmail.com
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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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