Multiplicity of periodic solutions for a boundary eigenvalue problem

2005 ◽  
Vol 20 (2) ◽  
pp. 223-232 ◽  
Author(s):  
Leonard Karshima Shilgba
Keyword(s):  
Eigenvalue Problem ◽  
Periodic Solutions ◽  
Boundary Eigenvalue

scholarly journals О неоднородных поляризованных состояниях вблизи точки фазового перехода в тонкой сегнетоэлектрической пленке

2018 ◽  
Vol 60 (7) ◽  
pp. 1322
Author(s):  
В.Н. Нечаев ◽  
А.В. Шуба
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Eigenvalue Problem ◽  
Film Thickness ◽  
Landau Theory ◽  
Polar Phase ◽  
Inhomogeneous Phase ◽  
Polar State ◽  
Boundary Eigenvalue ◽  
Phenomenological Landau Theory

AbstractIt is shown in terms of the phenomenological Landau theory of phase transitions that a phase transition to an inhomogeneous polar phase preceding in temperature a phase transition to a homogeneous polar state is possible. As a result of solving a boundary eigenvalue problem for the polarization equilibrium equation and electrostatics equations, wave vector k _⊥ characterizing the inhomogeneous phase has been determined and the temperature boundaries of its existence in the dependence on the film thickness and its surface properties have been found.

scholarly journals Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yu G. Smirnov ◽  
D. V. Valovik
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Eigenvalue Problem ◽  
Dispersion Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Effects ◽  
Kerr Nonlinearity ◽  
Anisotropic Layer ◽  
Boundary Eigenvalue ◽  
Made In

The problem of electromagnetic TM wave propagation through a layer with Kerr nonlinearity is considered. The layer is located between two half-spaces with constant permittivities. This electromagnetic problem is reduced to the nonlinear boundary eigenvalue problem for ordinary differential equations. It is necessary to find eigenvalues of the problem (propagation constants of an electromagnetic wave). The dispersion equation (DE) for the eigenvalues is derived. The DE is applied to nonlinear metamaterial as well. Comparison with a linear case is also made. In the nonlinear problem there are new eigenvalues and new eigenwaves. Numerical results are presented.

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