Physicists have taken a first step in understanding quantum emergence -- the transition from 'one-to-many' particles -- by studying not one, not many, but two isolated, interacting particles. The ...

Second harmonic generation is the lowest-order wave-wave nonlinear interaction occurring in, e.g., optical, radio, and magnetohydrodynamic systems. As a prototype behavior of waves, second harmonic ...

In this paper, we show the interaction phenomena about the first-order lump wave and multiple solitons by four theorems. The interaction phenomena are divided into two types, one type is absorbing ...