Bäcklund transformation and nonlinear superposition formula for the two-component short pulse equation

Abstract By means of the reciprocal transformation and the associated equation, a Bäcklund transformation (BT) containing both independent and dependent variables is worked out and studied for the two-component short pulse (2SP) equation. Based on it, the corresponding nonlinear superposition formula (NSF) is also constructed. Through reducing the BT and NSF of the 2SP equation, the BTs and NSFs for the SP equation, the focusing complex short pulse (cSP) equation and the defocusing cSP equation are obtained respectively. By analyzing the range of parameters in the solution, various solutions including soliton solitons, cuspon solitons, loop solitons, breather solutions are divided and their interaction are considered.