We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states.

• Received 20 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.254101