Optical patterns with different wavelengths.
The semiconductor resonator is an example of an optical system where two modulational instabilities with different wave numbers coexist. In the limit of nascent bistability, the dynamics is generically described by a nonvariational real order parameter equation, of which we give a detailed derivation. This considerably simplifies the linear and weakly nonlinear stability analyses. When the two instabilities are close together, we derive normal form equations and put special emphasis on "envelope" branches of solutions. These particular solutions may connect the two instability points or form an isola. On the basis of these rigorous results, we finally discuss the case of distant modulational instabilities, in both one and two transverse dimensions.
Kozyreff
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Oxford Centre for Industrial and Applied Mathematics, Oxford University, Oxford, OX1 SLB, United Kingdom. kozyreff@maths.ox.ac.uk
Tlidi
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