By N -soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate resonances of solitons in one-dimensional space. An asymmetric can be formed by adjusting distance between two molecule small enough. The interactions a...

We study how to generate binary de Bruijn sequences efficiently from the class of simple linear feedback shift registers with function $f(x_0, x_1, \ldots, x_{n-1}) = x_0 + x_1 x_{n-1}$ for $n \geq 3$, using cycle joining method. Based on properties this LFSRs, we propose two new generic successor rules, each which produces at least $2^{n-3}$ sequences. These classes build upon a framework prop...