Justification of amplitude equations



Invited articles:
abstract download J. Belmonte-Beitia and D. Pelinovsky, Bifurcation of gap solitons in periodic potentials with a periodic sign-varying nonlinearity coefficient, Applicable Analysis, 89, 1335-1350 (2010)
abstract download D.E. Pelinovsky, Asymptotic reductions of the Gross-Pitaevskii equation, Emergent Nonlinear Phenomena in Bose-Einstein Condensates, Eds. P.G. Kevrekidis, D.J. Franzeskakis, and R. Carretero-Gonzalez, Springer-Verlag, New York, pp. 377-398 (2008)





Regular papers:
abstract download D.E. Pelinovsky and D.V. Ponomarev, Justification of a nonlinear Schrodinger model for laser beams in photopolymers, Z. Angew. Math. Phys. 65, 405-433 (2014)
abstract download D. Pelinovsky and G. Schneider, Rigorous justification of the short-pulse equation, Nonlinear Differential Equations and Applications 20, 1277-1294 (2013)
abstract download D.E. Pelinovsky and T.Phan, Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation, Journal of Differential Equations 253, 2796-2824 (2012)
abstract download T. Dohnal and D. Pelinovsky, Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential, Physical Review E 85, 026605 (6 pages) (2012)
abstract download M. Coles and D. Pelinovsky, Loops of energy bands for Bloch waves in optical lattices, Studies in Applied Mathematics 128, 300-336 (2012)
abstract download E.W. Kirr, P.G. Kevrekidis, and D.E. Pelinovsky, Symmetry-breaking bifurcation in the nonlinear Schrodinger equation with symmetric potentials, Commun. Math. Phys. 308, 795-844 (2011)
abstract download D. Pelinovsky and G. Schneider, Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential, Journal of Differential Equations 248, 837-849 (2010)
abstract download T. Dohnal, D. Pelinovsky, and G. Schneider, Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential, Journal of Nonlinear Science, 19, 95-131 (2009)
abstract download D. Pelinovsky and G. Schneider, Moving gap solitons in periodic potentials, Mathematical Methods in the Applied Sciences 31, 1739-1760 (2008)
abstract download D. Pelinovsky, G. Schneider, and R. MacKay Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential, Communications in Mathematical Physics, 284, 803-831 (2008)
abstract download D. Pelinovsky and G. Schneider, Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential, Applicable Analysis 86, 1017-1036 (2007)