Numerical computation of localized waves in nonlinear lattices


    Solitary waves and fronts


  • G. James, Periodic travelling waves and compactons in granular chains, J. Nonlinear Sci. 22 (2012), 813-848.

    Original publication available at link.springer.com. Preprint available on arXiv: pdf file.


  • G. James and D. Pelinovsky, Gaussian solitary waves and compactons in Fermi-Pasta-Ulam lattices with Hertzian potentials, Proc. R. Soc. A. 470 (2165), 2014.

    Original publication available at royalsocietypublishing.org. Preprint available on arXiv: pdf file.


  • J.E. Morales, G. James and A. Tonnelier, Traveling waves in a spring-block chain sliding down a slope, Phys. Rev. E 96, 012227 (2017).

    Original publication available at aps.org. Preprint available on HAL: pdf file.


  • J.E. Morales, G. James and A. Tonnelier, Solitary waves in the excitable Burridge-Knopoff model, Wave Motion 76 (2018), 103-121.

    Original publication available at www.sciencedirect.com. Preprint available on: HAL.



    Solitary waves and traveling breathers in a strongly nonlinear lattice with phase invariance


  • G. James, Traveling breathers and solitary waves in strongly nonlinear lattices, to appear in Philosophical Transactions of the Royal Society of London A (2018), DOI 10.1098/rsta.2017.0138.


    Traveling breathers in Klein-Gordon lattices


  • Y. Sire and G. James, Numerical computation of travelling breathers in Klein-Gordon chains, Physica D 204 (2005), p. 15-40.

    Original publication available at www.sciencedirect.com. pdf file



    Breathers for fractional-order nonlinearities and nonsmooth systems


  • G. James, P.G. Kevrekidis and J. Cuevas, Breathers in oscillator chains with Hertzian interactions, Physica D 251 (2013), 39-59.

    Original publication available at www.sciencedirect.com. pdf file.


  • G. James and Y. Starosvetsky, Breather solutions of the discrete p-Schrödinger equation, in Localized Excitations in Nonlinear Complex Systems, Eds. R. Carretero-Gonzalez, J. Cuevas-Maraver, D. Frantzeskakis, N. Karachalios, P. Kevrekidis, F. Palmero-Acebedo, Nonlinear Systems and Complexity 7 (2014), 77-115, Springer.

    Original publication available at link.springer.com. Preprint available on arXiv: pdf file.


  • G. James, V. Acary and F. Pérignon, Periodic motions of coupled impact oscillators, to appear in Advanced Topics in Nonsmooth Dynamics: Transactions of the European Network for Nonsmooth Dynamics, R. Leine, V. Acary and O. Brüls, Eds., Springer (2018).

    Preprint available on: HAL.



    Breathers (bright or dark) for smooth nonlinearities


  • B. Sanchez-Rey, G. James, J. Cuevas and J.F.R. Archilla, Bright and dark breathers in Fermi-Pasta-Ulam lattices, Phys. Rev. B 70, 014301 (2004).

    Original publication available at www.aps.org. pdf file


  • G. James and M. Kastner, Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain, Nonlinearity 20 (2007), p. 631-657.

    Original publication available at www.iop.org. pdf file


  • G. James, A. Levitt and C. Ferreira, Continuation of discrete breathers from infinity in a nonlinear model for DNA breathing, Applicable Analysis 89 (2010), 1447-1465.

    Original publication available at www.tandfonline.com. pdf file



    Dark breathers in granular metamaterials


  • L. Liu, G. James, P. Kevrekidis and A. Vainchtein, Breathers in a locally resonant granular chain with precompression, Physica D 331 (2016), 27-47.

    Original publication available at www.sciencedirect.com. Preprint available on arXiv: pdf file.


  • L. Liu, G. James, P. Kevrekidis and A. Vainchtein, Strongly nonlinear waves in locally resonant granular chains, Nonlinearity 29 (2016), 3496-3527.

    Original publication available at iop.org. Preprint available on arXiv: pdf file.



    Breathers in presence of lattice defects


  • G. James, B. Sŕnchez-Rey and J. Cuevas, Breathers in inhomogeneous lattices : an analysis via centre manifold reduction, Reviews in Mathematical Physics 21 (2009), 1-59.

    Original publication available at www.worldscientific.com. pdf file



    Surface modes


  • G. James, J. Cuevas and P.G. Kevrekidis, Breathers and surface modes in oscillator chains with Hertzian interactions, Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications (NOLTA 2012), Palma, Majorca, Spain, 22-26 Oct. 2012, p. 470-473.

    Preprint available on arXiv: pdf file.



    Vortices in discrete cubic NLS


  • J. Cuevas, G. James, P. Kevrekidis and K. Law, Vortex solutions of the discrete Gross-Pitaevskii equation starting from the anti-continuum limit, Physica D 238 (2009), 1422-1431.

    Original publication available at www.sciencedirect.com. pdf file