Abstract
A
bstract
We find infinitely many soliton-like solutions in a deformation of the sine-Gordon theory in (
d
+ 1)-dimensional AdS
d
+1
(anti-de Sitter) spacetime for
d
≥ 2, as well as single solitonic solutions in dS
d
+1
(de Sitter) and H
d
+1
(Lobachevsky) spaces for
d
≥ 1 and in AdS
2
. We also find a deformation of the kink solution in scalar field theory with a polynomial potential in AdS
2
. The deformation of the theories are due to a coupling of the fields to the curvature of the background space-time. In the infinite radius limit, single soliton solutions reduce to solitons in flat space. Meanwhile, the multisoliton solution in AdS
d
+1
for
d
≥ 2 for certain values of the parameters reduces in the same limit to a single soliton solution boosted in the normal direction. However, there are also multisoliton solutions in AdS
d
+1
for
d
≥ 2 that do not have a flat space limit. In all cases we consider, gravity is not dynamical, and the background space remains strictly equal to either AdS
d
+1
, dS
d
+1
, or H
d
+1
, respectively.