We investigate the presence of defects in systems described by real scalar field in $(D,1)$ spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for $D$ arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in $D$ dimensions via soluble problems in $D=1$. We illustrate the procedure examining specific models and finding explicit solutions.

• Received 3 June 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.241601