Rogue periodic waves of the sine-Gordon equation

Abstract The rogue periodic wave solutions of the nonlinear Schrodinger equation and the modified KdV equation were discovered in 2018. The phenomenon of rogue periodic wave is new and very interesting, but little research has been done. In this letter, the rogue periodic wave solutions of the sine–Gordon equation are constructed by means of the Darboux transformation and the nonlinearization method. As an illustrative example, the exact formulas of first-and second-order rogue periodic waves are obtained.

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