Unconventional characteristic line for the nonautonomous KP equation

The unconventional characteristic line for a nonautonomous KP equation is constructed, which reveals that the propagation of solitons can be different from the traditional ones. Based on the Painlevé analysis and bilinear method, we obtain the soliton solution, and further study the polarity of characteristic line, the effect of initial phase, as well as the inelastic interaction and soliton resonance. We expect these results to be helpful in understanding relevant phenomena in water waves and dust acoustic waves.