Common Hirota Form Bäcklund Transformation for the Unified Soliton System

Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka

We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) $\cong$ GL(2,$\mathbb{R}$) $\cong$ Möbius group point of view, which might be a keystone to exactly solve so…