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We report results of the first global three-dimensional magnetohydrodynamicsimulations of the waves excited in an accretion disc by a rotating star with adipole magnetic field misaligned from the star's rotation axis (which isaligned with the disc axis). The main results are the following: (1) If themagnetosphere of the star corotates approximately with the inner disc, then weobserve a strong one-armed bending wave (a warp). This warp corotates with thestar and has a maximum amplitude between corotation radius and the radius ofthe vertical resonance. The disc's center of mass can deviate from theequatorial plane up to the distance of z_w\approx 0.1 r. However, the effectiveheight of the warp can be larger, h_w \approx 0.3 r due to the finite thicknessof the disc. Stars with a range of misalignment angles excite warps. However,the amplitude of the warps is larger for misalignment angles between 15 and 60degrees. (2) If the magnetosphere rotates slower, than the inner disc, then abending wave is excited at the disc-magnetosphere boundary, but does not form alarge-scale warp. Instead, high-frequency oscillations become strong at theinner region of the disc. These are (a) trapped density waves which form insidethe radius where the disc angular velocity has a maximum, and (b) inner bendingwaves which appear in the case of accretion through magnetic Raleigh-Taylorinstability. These two types of waves are connected with the inner disc andtheir frequencies will vary with accretion rate. Bending oscillations at lowerfrequencies are also excited including global oscillations of the disc. Incases where the simulation region is small, slowly-precessing warp forms.Simulations are applicable to young stars, cataclysmic variables, and accretingmillisecond pulsars.

Warps, bending and density waves excited by rotating magnetized stars: results of global 3D MHD simulations