High-frequency soliton-like waves in a relaxing medium

A nonlinear evolution equation is suggested to describe the propagation of waves in a relaxing medium. It is shown that for low-frequency approach this equation is reduced to the KdVB equation. The high-frequency perturbations are described by a new nonlinear equation. This equation has ambiguous looplike solutions. It is established that a dissipative term, with a dissipation parameter less than some limit value, does not destroy these looplike solutions. (C) 1999 American Institute of Physics. [S0022-2488(99)00503-4].