The shifted parity and delayed time-reversal symmetry-breaking solutions for the (1+1)-dimensional Alice–Bob Boussinesq equation - Dong, Peng; Ma, Zheng-Yi; Fei, Jin-Xi; Cao, Wei-Ping (Frontiers in Physics, 2023)
The integrable Alice-Bob system with the shifted parity and delayed time reversal is presented through the Lax pair for the (1+1)-dimensional Boussinesq equation. After introducing an extended Backlund transformation, this system shows abundant exact solutions with the auxiliary functions consisting of the hyperbolic functions or rational functions. The corresponding soliton structures contain the line solitons, breathers and lumps, which are all satised the shifted parity and delayed time reversal symmetry for the states of Alice A and Bob B. In particular, some lower circumstances can be expressed through their explicit solutions and their dynamic structures.