New interaction solutions of multiply periodic, quasi-periodic and non-periodic waves for the (n + 1)-dimensional double sine-Gordon equations

New exact solutions with built-in arbitrary functions for the (n + 1)-dimensional double sine-Gordon equation are studied by means of auxiliary solutions of the cubic nonlinear Klein-Gordon (CNKG) fields. By a proper selection of the arbitrary functions and the appropriate solutions of the CNKG systems, new solutions including periodic-solitoffs, periodic-twisted kinks, quasi-periodic and non-periodic waves are obtained.