In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and travelingwave solutions of the (2+1)-dimensional sine-Gordon equation are constructed. The traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a similar manner. Meanwhile, conservation laws are derived.
Wang, Gangwei; Yang, Kaitong; Gu, Haicheng; Guan, Fei; and Kara, A. H., "A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions" (2020). Mathematical and Statistical Sciences Faculty Publications and Presentations. 29.
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Nuclear Physics B