0
2013
Impact Factor

# Klaus Schneider

Mohrenstr. 39, 10117, Berlin, Germany
Weierstrass Institute for Applied Analysis and Stochastics

## Publications:

 Nefedov N. N., Recke L., Schneider K. R. Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems 2010, vol. 15, no. 2-3, pp.  382-389 Abstract We consider singularly perturbed semilinear parabolic periodic problems and assume the existence of a family of solutions. We present an approach to establish the exponential asymptotic stability of these solutions by means of a special class of lower and upper solutions. The proof is based on a corollary of the Krein–Rutman theorem. Keywords: singularly perturbed parabolic Dirichlet problems, exponential asymptotic stability, Krein–Rutman theorem, lower and upper solutions Citation: Nefedov N. N., Recke L., Schneider K. R.,  Asymptotic stability via the Krein–Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems, Regular and Chaotic Dynamics, 2010, vol. 15, no. 2-3, pp. 382-389 DOI:10.1134/S1560354710020231
 Gonchenko S. V., Schneider K. R., Turaev D. V. Quasiperiodic regimes in multisection semiconductor lasers 2006, vol. 11, no. 2, pp.  213-224 Abstract We consider a mode approximation model for the longitudinal dynamics of a multisection semiconductor laser which represents a slow-fast system of ordinary differential equations for the electromagnetic field and the carrier densities. Under the condition that the number of active sections $q$ coincides with the number of critical eigenvalues we introduce a normal form which admits to establish the existence of invariant tori. The case $q=2$ is investigated in more detail where we also derive conditions for the stability of the quasiperiodic regime Keywords: multisection semiconductor laser, averaging, mode approximation, invariant torus, normal form, stability Citation: Gonchenko S. V., Schneider K. R., Turaev D. V.,  Quasiperiodic regimes in multisection semiconductor lasers , Regular and Chaotic Dynamics, 2006, vol. 11, no. 2, pp. 213-224 DOI: 10.1070/RD2006v011n02ABEH000346