Positive energy singularities induced by Sine-Gordon solitons in (1+1)
-dimensional dilaton gravity with positive and negative cosmological c
onstant are considered. When the cosmological constant is positive, th
e singularities combine a white hole, a timelike singularity and a bla
ck hole joined smoothly near the soliton centre. When the cosmological
constant is negative, the solutions describe two timelike singulariti
es joined smoothly near the soliton centre. We describe these spacetim
es and examine their evaporation in one-loop approximation.