Time-dependent defects in integrable soliton equations.

We study (1 + 1)-dimensional integrable soliton equations with time-dependent defects located at  = (), where () is a function of class . We define the defect condition as a Bäcklund transformation evaluated at  = () in space rather than over the full line. We show that such a defect condition does not spoil the integrability of the system.

A new two-component integrable system with peakon solutions.

A new two-component system with cubic nonlinearity and linear dispersion: [Formula: see text]where is an arbitrary real constant, is proposed in this paper. This system is shown integrable with its Lax pair, bi-Hamiltonian structure and infinitely many conservation laws. Geometrically, this system describes a non-trivial one-parameter family of pseudo-spherical surfaces.