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We construct rogue wave solutions on the double periodic background for theHirota equation through one fold Darboux transformation formula. We considertwo types of double periodic solutions as seed solutions. We identify thesquared eigenfunctions and eigenvalues that appear in the one fold Darbouxtransformation formula through an algebraic method with two eigenvalues. Wethen construct the desired solution in two steps. In the first step, we createdouble periodic waves as the background. In the second step, we build roguewave solution on the top of this double periodic solution. We present thelocalized structures for two different values of the arbitrary parameter eachone with two different sets of eigenvalues.

Rogue waves on the double periodic background in Hirota equation