Soliton Solution and Its Property of Unstable Nonlinear Schrödinger Equation

A nonlinear evolution equation i u x + u t t +κ| u | 2 u =0, κ>0, is derived from unstable Sine-Gordon equation u t t }- u x x - m 2 sin u =0. The former nonlinear evolution equation, which we call unstable nonlinear Schrödinger equation, is solved by the inverse scattering method. It is shown that the position shifts for fast (slow) solitons, arising from their mutual collisions, are negative (positive). This is a property common to both nonlinear evolution equations.