The semistrong limit of multipulse interaction in a thermally driven optical system (original) (raw)
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Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators
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We derive a perturbed parametrically forced nonlinear Schrödinger equation to model pulse evolution in an optical parametric oscillator with absorption-induced heating. We apply both a rigorous renormalization group (RG) technique and the formal Wilsonian renormalization group to obtain a low-dimensional system of equations which captures the mutual interaction of pulses as well as their response to the thermally induced potential.
SIAM Journal on Mathematical Analysis, 2007
We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semistrong regime of two-pulse interactions in a regularized Gierer-Meinhardt system. In the semistrong limit the localized activator pulses interact strongly through the slowly varying inhibitor. The interaction is not tail-tail as in the weak interaction limit, and the pulse amplitudes and speeds change as the pulse separation evolves on algebraically slow time scales. In addition the point spectrum of the associated linearized operator evolves with the pulse dynamics. The RG approach employed here validates the interaction laws of quasi-steady two-pulse patterns obtained formally in the literature, and establishes that the pulse dynamics reduce to a closed system of ordinary differential equations for the activator pulse locations. Moreover, we fully justify the reduction to the nonlocal eigenvalue problem (NLEP) showing that the large difference between the quasi-steady NLEP operator and the operator arising from linearization about the pulse is controlled by the resolvent.
2005
We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semi-strong regime of two-pulse interactions in a regularized Gierer-Meinhardt system. In the semi-strong limit the strongly localized activator pulses interact through the weakly localized inhibitor, the interaction is not tail-tail as in the weak interaction limit, and the pulses change amplitude and even stability as their separation distance evolves on algebraically slow time scales. The RG approach employed here validates the interaction laws of quasi-steady pulse patterns obtained formally in the literature, and establishes that the pulse dynamics reduce to a closed system of ordinary differential equations for the activator pulse locations. Moreover, we fully justify the reduction to the nonlocal eigenvalue problem (NLEP) showing the large difference between the quasi-steady NLEP operator and the operator arising from linearization about the pulse is controlled by the resolvent. 2...
Physical Review A
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