Modulation equations : derivation and dynamics


    Discrete p-Schrödinger equation


  • G. James, Nonlinear waves in Newton's cradle and the discrete p-Schrödinger equation, Math. Models Meth. Appl. Sci. 21 (2011), 2335-2377.

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


  • 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.


  • B. Bidégaray-Fesquet, E. Dumas and G. James, From Newton's cradle to the discrete p-Schrödinger equation, SIAM J. Math. Anal. 45 (2013), 3404-3430.

    Original publication available at epubs.siam.org. Preprint available on arXiv: 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.


  • 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.


  • 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.


    Logarithmic KdV equation


  • 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.



    From granular metamaterials to cubic NLS


  • 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.



    From diatomic FPU lattice to coupled (stationary) NLS equations


  • 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



    Floquet spectrum for Rogue waves in NLS


  • J. Cuevas-Maraver, P. G. Kevrekidis, D. J. Frantzeskakis, N. I. Karachalios, M. Haragus and G. James, Floquet analysis of Kuznetsov--Ma breathers: A path towards spectral stability of rogue waves, Phys. Rev. E 96, 012202 (2017).

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



    Breathers and vortices in discrete cubic NLS


  • J. Cuevas, G. James, P. Kevrekidis, B. Malomed and B. Sànchez-Rey, Approximation of solitons in the discrete NLS equation, Journal of Nonlinear Mathematical Physics 15, supplement 3 (2008), 124-136.

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


  • 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