Breather solutions of the discrete p-Schr\'odinger equation

1^+), we introduce a continuum limit connecting the stationary DpS and logarithmic nonlinear Schr\"odinger equations. In this limit, breathers correspond asymptotically to Gaussian homoclinic solutions. We numerically analyze the stability properties of breather solutions depending on their even- or odd-parity symmetry. A perturbation of an unstable breather generally results in a translational motion (traveling breather) when alpha is close to unity, whereas pinning becomes predominant for larger values of alpha.
Comment: To appear in Springer Series on Wave Phenomena -->
Druh dokumentu: Working Paper
DOI: 10.1007/978-3-319-02057-0_4
Přístupová URL adresa: http://arxiv.org/abs/1307.8324
Přírůstkové číslo: edsarx.1307.8324
Autor: James, Guillaume, Starosvetsky, Yuli
Rok vydání: 2013
Předmět:
Druh dokumentu: Working Paper
DOI: 10.1007/978-3-319-02057-0_4
Popis: We consider the discrete p-Schr\"odinger (DpS) equation, which approximates small amplitude oscillations in chains of oscillators with fully-nonlinear nearest-neighbors interactions of order alpha = p-1 >1. Using a mapping approach, we prove the existence of breather solutions of the DpS equation with even- or odd-parity reflectional symmetries. We derive in addition analytical approximations for the breather profiles and the corresponding intersecting stable and unstable manifolds, valid on a whole range of nonlinearity orders alpha. In the limit of weak nonlinearity (alpha --> 1^+), we introduce a continuum limit connecting the stationary DpS and logarithmic nonlinear Schr\"odinger equations. In this limit, breathers correspond asymptotically to Gaussian homoclinic solutions. We numerically analyze the stability properties of breather solutions depending on their even- or odd-parity symmetry. A perturbation of an unstable breather generally results in a translational motion (traveling breather) when alpha is close to unity, whereas pinning becomes predominant for larger values of alpha.
Comment: To appear in Springer Series on Wave Phenomena
Databáze: arXiv