“…Eq. ( 1) arises in many different physical contexts, such as acoustic wave and phonons in a certain anharmonic lattice [3,4], Alfvén wave in a cold collision-free plasma [5,6], thin elastic rods [7], meandering ocean currents [8], dynamics of traffic flow [9,10], hyperbolic surfaces [11], slag-metallic bath interfaces [15], and Schottky barrier transmission lines [16]. The well-known Miura transform [2,12] u(x, t) = −σq 2 (x, t) + √ σq x (x, t) established the relation between Eq.…”