Bilinearization of Soliton Equations

Transformations of soliton equations into the bilinear forms involving four dependent variables are discussed. It is found that both nonlinear Schrödinger equation and classical Heisenberg ferromagnet equation are transformed into the same bilinear from, while the equation {aligned} φₓₜ{=}φ(1-|φₜ|²)1/2 {aligned} shares the same bilinear form with the Pohlmeyer-Lund-Regge-Getmanov equation. Transformations of the complex sine-Gordon equation and the Landau-Lifshitz equation into the bilinear forms are also described.