Mathematics and Computers in Simulation 69 (2005) 346–355 Cavity soliton mobility in semiconductor microresonators R. Kheradmand a,c , L.A. Lugiato a , G. Tissoni a, ∗ , M. Brambilla b , H. Tajalli c a INFM, Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Universit` a dell’Insubria, via Valleggio 11, 22100 Como, Italy b INFM, Dipartimento di Fisica Interateneo, Universit` a e Politecnico di Bari, via Orabona 4, 70126 Bari, Italy c Center for Applied Physics and Astronomical Research, University of Tabriz, Tabriz 51664-163, Iran Available online 26 February 2005 Abstract We show here different methods to demonstrate the intrinsic mobility of cavity solitons and realize a number of cavity soliton trajectories. These methods are based on one hand, on the drift of cavity solitons in phase or amplitude gradients and on the other hand, on the recently discovered spontaneous motion of cavity solitons induced by the thermal dynamics in semiconductor devices. When the holding beam corresponds to a doughnut mode (instead of a Gaussian as usually) cavity solitons undergo a rotational motion along the annulus of the doughnut. In a similar way, thermal motion can be controlled by introducing phase or amplitude modulations in the holding beam. Finally, we show that in presence of a weak 2D phase modulation, the cavity soliton, due to the thermally induced motion, performs a random walk from one maximum of the profile to another, always escaping from the temperature minimum generated by the soliton itself (fugitive soliton). © 2005 IMACS. Published by Elsevier B.V. All rights reserved. PACS: 42.65.Sf; 42.70.Nq; 42.65.Tg Keywords: Cavity solitons; Pattern formation; Transverse effects in nonlinear systems; Semiconductor amplifiers 1. Introduction Applications to information technology are one of the goals of the extensive work in the field of transverse patterns formation in nonlinear optical systems [1–6]. The problem of the correlation among ∗ Corresponding author. Tel.: +39 031 2386276; fax: +39 031 2386209. E-mail address: giovanna.tissoni@mi.infn.it (G. Tissoni). 0378-4754/$30.00 © 2005 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2005.01.008