Publications and preprints

(sorted by topic)






Nonlinear waves in granular chains

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.

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.

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, 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, 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.

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, 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.



Continuation of localized oscillations (breathers) from infinity

G. James and D. Pelinovsky, Breather continuation from infinity in nonlinear oscillator chains, Discrete and Continuous Dynamical Systems A 32 (2012), 1775-1799.
     Original publication available at www.aimsciences.org. Preprint available on arXiv: 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



Localized oscillations in DNA

M. Peyrard and G. James, Intrinsic localized modes in nonlinear models inspired by DNA, Nonlinear Theory and its Applications (NOLTA), Vol. 3 (2012), 27-51.
     Original publication available at www.nolta.ieice.org. pdf file

M. Peyrard, S. Cuesta-Lopez and G. James, Nonlinear analysis of the dynamics of DNA breathing, Journal of Biological Physics 35 (2009), 73-89.
     Original publication available at www.springerlink.com. pdf file

M. Peyrard, S. Cuesta-Lopez and G. James, Modelling DNA at the mesoscale : a challenge for nonlinear science ? Nonlinearity 21 (2008), T91-T100.
     Original publication available at iop.org. pdf file



Mechanical and ionic waves along actin filaments

C. Ferreira, G. James and M. Peyrard, Nonlinear lattice models for biopolymers: dynamical coupling to a ionic cloud and application to actin filaments, Discrete and Continuous Dynamical Systems S 4 (2011), 1147-1166.
     Original publication available at aimsciences.org. pdf file



Periodic and relative periodic orbits in Euclidean-invariant Hamiltonian systems
(classical Hamiltonians for planar molecules and atomic clusters)


G. James, P. Noble and Y. Sire, Continuation of relative periodic orbits in a class of triatomic Hamiltonian systems, Ann. IHP, Analyse non linéaire 26 (2009), 1237-1264.
     Original publication available at www.sciencedirect.com. pdf file

G. James and P. Noble, Weak coupling limit and localized oscillations in Euclidean invariant Hamiltonian systems, J. Nonlinear Sci. 18 (2008), p. 433-461.
     Original publication available at www.springerlink.com. pdf file



Center manifold theorem for infinite-dimensional maps (James, J. Nonlinear Sci. 2003)
Applications : existence theorems for time-periodic localized waves (breathers) and dark solitons in oscillator chains

G. James, B. Sànchez-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

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 and P. Noble, Breathers on diatomic Fermi-Pasta-Ulam lattices, Physica D 196 (2004), p. 124-171.
    Original publication available at www.sciencedirect.com. pdf file

G. James and P. Noble, Breathers on diatomic FPU chains with arbitrary masses, proceedings of the third conference on Localization and Energy Transfer in Nonlinear Systems, San Lorenzo de El Escorial, Spain, 17-21 June 2002, L. Vazquez, R.S. MacKay, M.P. Zorzano Eds., World Scientific (2003), p. 225-232.

G. James, A centre manifold technique for computing time-periodic oscillations in infinite lattices, proceedings of the third conference on Localization and Energy Transfer in Nonlinear Systems, San Lorenzo de El Escorial, Spain, 17-21 June 2002, L. Vazquez, R.S. MacKay, M.P. Zorzano Eds., World Scientific (2003), p. 202-209.
    Original publication available at www.worldscientific.com. pdf file

G. James, Centre manifold reduction for quasilinear discrete systems, J. Nonlinear Sci., vol. 13, n° 1 (2003), p. 27-63.
    Original publication available at www.springerlink.com. pdf file

G. James, Existence of breathers on FPU lattices, C. R. Acad. Sci. Paris, t. 332, Serie I (2001), p. 581-586.
    Original publication available at www.sciencedirect.com. pdf file



Reviews on center manifold methods for lattice differential equations

G. James and Y. Sire, Center manifold theory in the context of infinite one-dimensional lattices, in : The Fermi-Pasta-Ulam Problem. A Status Report, G. Gallavotti Ed., Lecture Notes in Physics 728 (2008), p. 207-238.
     Original publication available at www.springerlink.com. pdf file

G. James, Ondes non linéaires en milieu discret, Habilitation Thesis, Université Paul Sabatier Toulouse 3 (December 2005).
     Manuscript (in French) : pdf file



Systems of advance-delay differential equations
Existence theorems for oscillating solitary waves (travelling breathers) in oscillator chains

G. Iooss and G. James, Localized waves in nonlinear oscillator chains, Chaos 15 (2005), 015113.
    Original publication available at www.aip.org. pdf file

G. James and Y. Sire, Travelling breathers with exponentially small tails in a chain of nonlinear oscillators, Commun. Math. Phys. 257 (2005), p. 51-85.
    Original publication available at www.springerlink.com. pdf file

Y. Sire and G. James, Ondes solitaires pulsatoires en milieu discret, 8ème Rencontre du Non-Linéaire, IHP, Paris, 9-11 March 2005, R. Ribotta Ed., éditions Non Linéaire Publications (2005), p. 247-252. pdf file

Y. Sire and G. James, Travelling breathers in Klein-Gordon chains, C. R. Acad. Sci. Paris, t. 338, Serie I (2004) p. 661-666.
    Original publication available at www.sciencedirect.com. pdf file



Numerical studies of localized structures (stationary or travelling breathers, dark solitons, vortices) in spatially discrete systems, and their approximations

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

J. Cuevas, G. James, P.G. Kevrekidis and K.J.H. Law, Vortex Solutions of the Defocusing Discrete Nonlinear Schrödinger Equation, International Conference on Numerical Analysis and Applied Mathematics, Rethymno, Crete, 18-22 September 2009, T.E. Simos, G. Psihoyios, Ch. Tsitouras Eds., AIP Conf. Proc. 1168 (2009), p. 135-138.
     Original publication available at aip.org. pdf file

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

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

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

B. Sanchez-Rey, J.F.R. Archilla, G. James and J. Cuevas, Breathers in FPU systems, near and far from the phonon band, proceedings of the third conference on Localization and Energy Transfer in Nonlinear Systems, San Lorenzo de El Escorial, Spain, 17-21 June 2002, L. Vazquez, R.S. MacKay, M.P. Zorzano Eds., World Scientific (2003), p.342-343.
    Original publication available at www.worldscientific.com. Preprint available on arXiv: pdf file.



Internal travelling waves in density stratified fluids (Euler equation) : existence theorems, convergence near a singular two-layer limit

G. James, Internal Travelling Waves in the Limit of a Discontinuously Stratified Fluid, Arch. Rational Mech. Anal., vol. 160, n° 1 (2001), p. 41-90.
    Original publication available at www.springerlink.com. pdf file

G. James, Passage à la limite vers un modèle à deux couches dans le problème des ondes progressives 2D en fluide continûment stratifié, Rencontre du Non-Linéaire 1999, IHP Paris, Paris-Onze éditions, p. 125-130.

G. James, Réduction à une variété centrale du problème des ondes progressives en fluide continûment stratifié, dans la limite d'une stratification discontinue, C. R. Acad. Sci. Paris, t. 327, Série I (1998), p. 699-704.
    Original publication available at www.springerlink.com. pdf file

G. James, Small amplitude steady internal waves in stratified fluids, Ann. Univ. Ferrara, Sez VII, Sc. Mat., Vol. XLIII (1997), p. 65-119.
    Original publication available at www.springerlink.com. pdf file