Abstract
We investigate a mathematical nonlinear-optics model that is a scalar parabolic equation on a circle with a small diffusion coefficient and a deviating spatial argument. We establish that the problem under consideration is characterized by the so-called buffering phenomenon, i.e., under an appropriate choice of the parameters, the coexistence of an arbitrary fixed number of time-periodic stable solutions of the problem can be obtained. We reveal the mechanisms for the occurrence of this phenomenon.
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REFERENCES
S. A. Akhmanov, M. A. Vorontsov, and V. Yu. Ivanov, “Generation of structures in optical systems with two-dimensional feedback: A way to create nonlinear-optical analogs of neural networks,” in: New Physical Principles in Optical Data Processing [in Russian] (S. A. Akhmanov and M. A. Vorontsov, eds.), Nauka, Moscow (1990), pp. 263–325.
A. V. Razgulin, Comput. Math. Math. Phys., 33, No. 1, 61–70 (1993).
A. L. Skubachevskij, Differ. Equ., 34, 1395–1402 (1998).
E. P. Belan, J. Math. Sci., New York, 107, 4437–4442 (2001).
E. P. Belan, Din. Sist., Simferopol', 17, 179–184 (2001).
Yu. S. Kolesov, Sb. Math., 78, 367–378 (1994).
Yu. S. Kolesov, “Stability and bifurcation of traveling waves,” in: Nonlinear Oscillations in Problems of Ecology [in Russian] (Yu. S. Kolesov, ed.), Yaroslavl State University, Yaroslavl (1985), pp. 3–10; A. N. Kulikov, “Analysis of conditions for stability of traveling waves,” ibid., pp. 103-107.
A. Yu. Kolesov, E. F. Mishchenko, and N. Kh. Rozov, Proc. Steklov Math. Inst., 222, 1–189 (1998).
A. Yu. Kolesov, N. Kh. Rozov, and V. G. Sushko, Fundam. Prikl. Mat., 5, 437–473 (1999); A. Yu. Kolesov, E. F. Mishchenko, and N. Kh. Rozov, Russ. Math. Surveys, 55, 297-321 (2000); A. Yu. Kolesov and N. Kh. Rozov, Proc. Steklov Math. Inst., 233, 143-196 (2001).
V. F. Kambulov, A. Yu. Kolesov, and N. Kh. Rozov, Comput. Math. Math. Phys., 38, 1233–1246 (1998); A. Yu. Kolesov and N. Kh. Rozov, Sb. Math., 191, 1147-1169 (2000).
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Kolesov, A.Y., Rozov, N.K. Optical Buffering and Mechanisms for Its Occurrence. Theoretical and Mathematical Physics 140, 905–917 (2004). https://doi.org/10.1023/B:TAMP.0000033028.08598.67
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DOI: https://doi.org/10.1023/B:TAMP.0000033028.08598.67