Abstract
This paper is concerned with the existence and properties of solutions of the following problem, The main results are Theorems 1 and 2 in section 2, establishing the existence of solutions having any prescribed number of zeros and with the further property that the zeros of u and u′ interlace. The solutions of (1.1)-(1.2) lead to a description of beams of light which, due to the nonlinearity of the medium in which they propagate, remain concentrated (self-trapped) near the axis of propagation. In any plane transverse to the axis of propagation the intensity of illumination is radially symmetric with respect to the axis and the zeros and turning points of u correspond to circles of zero and maximal intensity. Our analysis and conclusions are similar to those in [1] for another model for self-trapped light.
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McLeod, J.B., Stuart, C.A., Troy, W.C. (1992). An Exact Reduction of Maxwell’s Equations. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_26
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DOI: https://doi.org/10.1007/978-1-4612-0393-3_26
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