Self-trapping of an electromagnetic field and bifurcation from the essential spectrum

Akhmanov, R. V., Khokhlov, R. V. & Sukhorukov, A. P.: Self-focusing, self-defocusing and self-modulation of laser beams, in Laser Handbook, edited by F. T. Arecchi & E. O. Schulz Dubois, North-Holland, Amsterdam, 1972. Born, M. & Wolf, E.: Principles of Optics, fifth edition, Pergamon Press, Oxford, 1975. Brezis, H.: Analyse fonctionnelle, Masson, Paris, 1983. Chiao, R. Y., Garmire, E. & Townes, C. H.: Self-trapping of optical beams, Phys. Rev. Lett. 13 (1964), 479–482. Dunford, N. & Schwartz, J. T.: Linear Operators, Vol. 2, Interscience, New York, 1958. Feynman, R. P., Leighton, R. B. & Sands, M.: Lectures on Physics, Vol. 2, Addison-Wesley, New York, 1964. Hellwarth, R. W.: Third order susceptibilities of liquids and solids, Prog. Quantum Electr. 5 (1975), 1–68. Kato, T.: Perturbation Theory for Linear Operators, Springer, Berlin, 1976. Marburger, J. H.: Self-focusing: theory. Prog. Quant. Electr. 4 (1975), 35–100. Marburger, J., Huff, L., Reichert, L. D. & Wagner, W. S.: Stationary self-trapping of optical beams in dense media with Lorentz local-field corrections, Phys. Rev. 184 (1969), 255–259. Pohl, D.: Vectorial theory of self-trapping light beams, Optics Comm. 2 (1970), 305–308. Reintjes, J. F.: Nonlinear Optical Processes, in Encyclopedia of Physical Science and Technology, Vol. 9, Academic Press, New York, 1987. Shen, Y. R.: Self-focusing: experimental, Prog. Quant. Electr. 4 (1975), 1–34. Smith, W. L.: Nonlinear refractive index, in Handbook of Laser Science and Technology, Vol. 3, editor M. J. Weber, CRC Press, Boca Raton, 1986. Snyder, A. W. & Love, J. D.: Optical Waveguide Theory, Chapman and Hall, London, 1983. Strauss, W.: The nonlinear Schrödinger equation, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations, North Holland, Amsterdam, 1978. Strauss, W.: Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977), 149–162. Stuart, C. A.: Global properties of components of solutions of nonlinear second order ordinary differential equations on the half-line, Ann. Sc. Norm, Sup. Pisa 2 (1975), 265–286. Stuart, C. A.: Bifurcation for Dirichlet problems without eigenvalues, Proc. London Math. Soc. 45 (1982), 169–192. Stuart, C. A.: Bifurcation from the essential spectrum, Proc. of Equal. Diff. 82, Lecture Notes in Math. No. 1017, Springer, Berlin, 1983. Stuart, C. A.: Bifurcation from the essential spectrum for some non-compact non-linearities, Math. Meth. Appl. Sci. 11 (1989), 525–542. Svelto, O.: Self-focusing, self-trapping and self-phase modulation of laser beams, in Progress in Optics, Vol. 12, editor E. Wolf, North Holland, Amsterdam, 1974. Talanov, V. S.: Self-focusing of wave beams in nonlinear media, 564-JETP Lett. 2 (1965), 138–141. Wang, C. C.: Mathematical Principles of Mechanics and Electromagnetism, Part B, Plenum Press, New York, 1979. Stegeman, G. I., Ariyasu, J., Seaton, C. I., Shen, T-P., & Moloney, J. V.: Non-linear thin-film guided waves in non-Kerr media, Appl. Phys. Lett. 47 (1985), 1254–1256. Stegeman, G. I., Wright, E. M., Seaton, C. T., Moloney, J. V., Shen, T. P., Maradudin, A. A., & Wallis, R. F.: Nonlinear slab-guided waves in non-Kerr-like media, IEEE, J. Quantum Elect. 22 (1986), 977–983. Langbein, U., Lederer, F., Peschel. T., & Ponath, H.-E.: Nonlinear guided waves in saturable nonlinear media, Opt. Letter 10 (1985), 571–573.