  We consider the motion of a matter-wave bright soliton under the influence of
a cloud of thermal particles. In the ideal one-dimensional system, the
scattering process of the quasiparticles with the soliton is reflectionless,
however, the quasiparticles acquire a phase shift. In the realistic system of a
Bose-Einstein condensate confined in a tight waveguide trap, the transverse
degrees of freedom generate an extra but small nonlinearity in the system which
gives rise to finite reflection and leads to dissipative motion of the soliton.
We calculate the velocity and temperature-dependent frictional force and
diffusion coefficient of a matter wave bright soliton immersed in a thermal
cloud.
