  This work reports on calculations of the deformation energy of a nucleus plus
an emitted cluster as a soliton moving on its surface. The potential barrier
against the emission of a soliton is calculated within the
macroscopic-microscopic method. The outer turning point of the barrier
determines limitations on the geometrical and kinematical parameters for the
formation of a surface soliton. For large asymmetry, the two-center shell model
is used to assign a structure to the soliton. Calculations for
$^{248}$N\lowercase{o} with the emission of a $^{40}$C\lowercase{a} soliton are
reported; likewise for $^{224}$T\lowercase{h} with the emission of $^{16}$O.
Except for necked shapes at the very first stages of soliton formation, the
greatest portion of the deformation path displays rather compact configurations
with large neck radii. These shape sequences correspond to allowable soliton
velocities. Close to and just beyond the touching point configuration, where
the shape becomes concave, the width and the velocity of the soliton approach
zero. The calculations suggest that the emission of a $^{40}$C\lowercase{a}
structure is quite probable due to a low potential barrier, whereas the
emission of an $^{16}$O type soliton is rather unlikely due to the higher
penetration barrier.
