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Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions

Gervais Nazaire Beukam Chendjou, Jean Pierre Nguenang, Andrea Trombettoni, Thierry Dauxois, Ramaz Khomeriki, Stefano Ruffo
2018 Communications in nonlinear science & numerical simulation  
We study the dynamics of Fermi-Pasta-Ulam chains with both harmonic and anharmonic power-law long-range interactions. We show that the dynamics is described in the continuum limit by a generalized fractional Boussinesq differential equation, whose derivation is performed in full detail. We also discuss a version of the model where couplings are alternating in sign.
doi:10.1016/j.cnsns.2018.01.006 fatcat:koij5pvq3zcs7dsxvjqyk3fn64

Pulse solutions of the fractional effective models of the Fermi–Pasta–Ulam lattice with long-range interactions

Gervais Nazaire Beukam Chendjou, Jean Pierre Nguenang, Andrea Trombettoni, Thierry Dauxois, Ramaz Khomeriki, Stefano Ruffo
2019 Journal of Statistical Mechanics: Theory and Experiment  
One of authors, G N B Chendjou, acknowledges the hospitality of the Faculty of Exact and Natural Sciences of Ivane Javakhishvili Tbilisi State University of Tbilisi, Georgia, during November 13-26, 2017  ... 
doi:10.1088/1742-5468/ab47fd fatcat:thoeb27hyjfgrkevla2awmxs4m