The non-linear Schrödinger equation with a periodic δ-interaction View Full Text


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Article Info

DATE

2013-09

AUTHORS

Jaime Angulo Pava, Gustavo Ponce

ABSTRACT

We study the existence and stability of space-periodic standing waves for the space-periodic cubic nonlinear Schrödinger equation with a point defect determined by a space-periodic Dirac distributionat the origin. This equation admits a smooth curve of positive space-periodic solutions with a profile given by the Jacobi elliptic function of dnoidal type. Via a perturbationmethod and continuation argument, we prove that in the case of an attractive defect the standing wave solutions are stable in Hper1([−π, π]) with respect to perturbations which have the same space-periodic as the wave itself. In the case of a repulsive defect, the standing wave solutions are stable in the subspace of even functions of Hper1([−π, π]) and unstable in Hper1([−π, π]) with respect to perturbations which have the same space-periodic as the wave itself. More... »

PAGES

497-551

References to SciGraph publications

  • 1983-12. Nonlinear Schrödinger equations and sharp interpolation estimates in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1982-12. Orbital stability of standing waves for some nonlinear Schrödinger equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2007-08. Soliton Splitting by External Delta Potentials in JOURNAL OF NONLINEAR SCIENCE
  • 1971. Handbook of Elliptic Integrals for Engineers and Scientists in NONE
  • 2007-12. Orbital stability of periodic waves for the nonlinear Schrödinger equation in JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • 2007-08. Fast Soliton Scattering by Delta Impurities in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1988. Solvable Models in Quantum Mechanics in NONE
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    http://scigraph.springernature.com/pub.10.1007/s00574-013-0024-8

    DOI

    http://dx.doi.org/10.1007/s00574-013-0024-8

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