Bifurcation modes in a nonlinear optical system with distributed field rotation
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We consider a model of a nonlinear optical system with distributed field rotation described by a functional-differential diffusion equation. An existence theorem is proved for periodical spatially nonhomogeneous traveling-wave solutions, which are generated from a spatially homogeneous stationary solution by an Andronov-Hopf (cycle-generating) bifurcation. A series expansion of the solution in powers of a small parameter is obtained and a stability condition is given. Simulation results are used to discuss the properties of the model.
KeywordsMathematical Modeling Stability Condition Computational Mathematic Stationary Solution Industrial Mathematic
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- 1.S. A. Akhmanov, M. A. Vorontsov, and V. Yu. Ivanov, “Generation of structures in optical systems with two-dimensional feedback: toward nonlinear optical analogues of neuron networks,” in: S. A. Akhmanov and M. A. Vorontsov (eds.), New Physical Principles of Optical Information Processing [in Russian], Nauka, Moscow (1990), pp. 263–325.Google Scholar
- 4.J. L. Lions and E. Magenes, Nonhomogeneous Boundary Value Problems and Applications, Vol. 2, Springer (1972).Google Scholar
- 5.V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow (1980).Google Scholar
- 6.D. H. Sattinger, Topics in Stability and Bifurcation Theory, Lect. Notes Math., vol. 309 (1973).Google Scholar
- 7.V. I. Yudovich, Linearization Method in Hydrodynamic Stability Theory [in Russian], Izd. RostGU, Rostov-on-Don (1984).Google Scholar
- 8.T. Kato, Perturbation Theory of Linear Operators [Russian translation], Mir, Moscow (1972).Google Scholar
- 10.M. A. Vorontsov and A. V. Razgulin, “Properties of global attractor in a nonlinear optical system having nonlocal interactions,” Photonics and Optoelectronics,1, No. 2, 103–111 (1993).Google Scholar