Asymmetric bound states of differential equations in nonlinear optics

A. Ambrosetti; D. Arcoya; J. L. Gámez

Rendiconti del Seminario Matematico della Università di Padova (1998)

  • Volume: 100, page 231-247
  • ISSN: 0041-8994

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Ambrosetti, A., Arcoya, D., and Gámez, J. L.. "Asymmetric bound states of differential equations in nonlinear optics." Rendiconti del Seminario Matematico della Università di Padova 100 (1998): 231-247. <http://eudml.org/doc/108459>.

@article{Ambrosetti1998,
author = {Ambrosetti, A., Arcoya, D., Gámez, J. L.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Schrödinger equation; bifurcation; nonlinear optics; asymmetric solutions; Poincaré-Melnikov theory; homoclinics},
language = {eng},
pages = {231-247},
publisher = {Seminario Matematico of the University of Padua},
title = {Asymmetric bound states of differential equations in nonlinear optics},
url = {http://eudml.org/doc/108459},
volume = {100},
year = {1998},
}

TY - JOUR
AU - Ambrosetti, A.
AU - Arcoya, D.
AU - Gámez, J. L.
TI - Asymmetric bound states of differential equations in nonlinear optics
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1998
PB - Seminario Matematico of the University of Padua
VL - 100
SP - 231
EP - 247
LA - eng
KW - Schrödinger equation; bifurcation; nonlinear optics; asymmetric solutions; Poincaré-Melnikov theory; homoclinics
UR - http://eudml.org/doc/108459
ER -

References

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  1. [1] N.N. Akhmediev, Novel class of nonlinear surface waves: Asymmetric modes in a symmetric layered structure, Sov. Phys. JEPT, 56 (1982), pp. 299-303. 
  2. [2] A. Ambrosetti - M. Badiale, Homoclinics: Poincaré-Melnikov type results via a variational approach. Annales I.H.P. - Anal. Nonlin., to appear. Preliminary note on C. R. Acad. Sci. Paris, 323, Série I (1996), pp. 753-758. Zbl0887.34042MR1416171
  3. [3] A. Ambrosetti - M. Badiale, Variational perturbative methods and bifurcation of bound states from the essential spectrum, Preprint Scuola Normale Superiore, March 1997, to appear. Zbl0928.34029MR1664089
  4. [4] M. Grillakis - J. Shatah - W. Strauss, Stability theory of solitary waves in the presence of symmetry I and II, Jour. Funct. Anal., 74 (1987), pp. 160-197 and 94 (1990), pp. 308-348. Zbl0656.35122MR901236
  5. [5] C.K.R.T. Jones - J.V. Moloney, Instability of standing waves in nonlinear optical waveguides, Phys. Lett. A, 117 (1986), pp. 176-184. 
  6. [6] Y.G. Oh, On positive muLti-bump states of nonlinear Schrödinger equations under multipte well potentials, Comm. Math. Phys., 131 (1990), pp. 223-253. Zbl0753.35097MR1065671
  7. [7] C. Stuart, Guidance properties of nonlinear planar waveguides, Arch. Rational Mech. Analysis, 125 (1993), pp. 145-200. Zbl0801.35136MR1245069

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