Exactly solved BPS wall and winding number in N=1 Supergravity
  A BPS exact wall solution is found in N=1 supergravity in four dimensions. The model uses chiral scalar field with a periodic superpotential admitting winding numbers. Maintaining the periodicity in supergravity requires a gravitational correction to superpotential which allows the exact solution. By introducing boundary cosmological constants, we construct non-BPS multi-wall solutions for which a systematic analytic approximation is worked out for small gravitational coupling. 
Minoru Eto, Nobuhito Maru, Norisuke Sakai and Tsuyoshi Sakata