Variable separation solution and multi-valued soliton of an extended (3+1)-dimensional B-type Kadomtsev-Petviashvili equation

This paper obtains exponential variable separation solution of an extended (3+1)-dimensional B-type Kadomtsev-Petviashvili equation via the projective Riccati equation method(PREM), which is different from the multi-linear variable separation approach(MLVSA). The obtained solution possesses three arbitrary functions lambda(x,z), rho(y), tau(t), and covers many special cases, such as sin-cos,sinh-cosh,sech-tanh,sec-tan,csch-coth,csc-cot solutions. By introducing suitable functions, we analyze the head-on as well as chase-after collisions between two and three folded solitary waves. These folded waves have large multi-valued structures, such as one- and two-loop, embedded-bell, embedded-peak, and combined shapes that may help simulate complex folded appearance in real life. Moreover, through the asymptotic analysis, phase shifts and their difference during the interaction are given to dissect wave motion systematically.