The algebraic mapping relations between the(2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein–Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton and solitoff solutions are obtained, such as broken line shape, 'V' shape, 'snake' shape and 'M' shape solitary waves,Zigzag-curve type, 'ω' shape, peroidic-curve type, oscillatory Arch-type and parabolic shape bright soliton waves. We also investigate the propagating properties of some soliton solutions.
The algebraic mapping relations between the(2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein–Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton and solitoff solutions are obtained, such as broken line shape, 'V' shape, 'snake' shape and 'M' shape solitary waves,Zigzag-curve type, 'ω' shape, peroidic-curve type, oscillatory Arch-type and parabolic shape bright soliton waves. We also investigate the propagating properties of some soliton solutions.