Short note on the stability of a dilatonic wall

A nontopological soliton solution of dilaton-Maxwell theory describes a domain wall-like solution which confines magnetic flux in its core [G.W. Gibbons and C.G. Wells, Class. Quant. Grav. 11, 2499 (1994)]. Since the solution is not stabilized by a nontrivial topology of the vacuum manifold, it is interesting to see if the static solution is stable against small fluctuations. We consider the stability of the solution in response to small fluctuations in the scalar and magnetic fields. It is determined that the ansatz solution does indeed exhibit stability.