On 29-31 October 2003, numerous geosynchronous magnetopause crossings (GMCs) were identified using magnetic field data from two GOES satellites and plasma data from four Los Alamos National Laboratory (LANL) satellites. We can distinguish four long-lasting intervals, when geosynchronous satellites observed GMCs in a wide range of local time: at ∼0600-0900 UT 29 October; from ∼1000 UT 29 October to 0400 UT 30 October; from ∼1700 UT 30 October to ∼0800 UT 31 October, and at ∼1100-1300 UT 31 October. During a part of those intervals the GMCs occurred in the dawn and dusk sectors under northward interplanetary magnetic field (IMF) that indicates to magnetospheric compression by extremely high solar wind pressure. We found that at 0400-1000 UT 31 October the compression was accompanied with large-amplitude Pc5 pulsation, which can be attributed to global magnetospheric mode (cavity resonance). Multiple GMCs were revealed for the time interval of Pc5 pulsation occasion. An amplitude of the maghetopause oscillation in noon sector was estimated of about 0.26∼0.6 RE. An application of the maghetopause models enabled us studying the magnetopause dawn-dusk asymmetry, which was revealed on the main phase and in maximum of two great geomagnetic storms on 29 and 30 October. We shown that the asymmetry can be formally represented as a shifting of the dayside magnetopause toward the dusk on average distance of 0.2∼0.3 RE. Besides, in some cases the asymmetry was larger and required a shifting of about 0.4 R E. It was shown that the magnitude of the dawn-dusk asymmetry is related to the internal geomagnetic disturbances rather than to the external conditions in the IMF.