The nonlocal Alice–Bob solutions for an extended combination of the Kadomtsev–Petviashvili3 and the Kadomtsev–Petviashvili4 equations

The paper first introduces the Alice–Bob system for the extended combination of the Kadomtsev–Petviashvili3 and the Kadomtsev–Petviashvili4 equations (cKP3-4), which is an integrable model. Based on the extended Bäcklund transformation, this system exists bilinear form after introducing an auxiliary variable. In order to construct the special explicit solution, that is, to satisfy the principle of the ${\hat{P}}_s^x{\hat{P}}_s^y{\hat{T}}_{d}A=B$ symmetry, we present one universal auxiliary function. Thereafter, this function can deduce various types of symmetry breaking solutions, which contain different soliton structures.