Formation of rogue waves on the periodic background in a fifth-order nonlinear Schrödinger equation

We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and nonlinearization spectral problem, we generate solution two different periodic backgrounds. analyze obtained for values system parameter point out certain novel features our results. also compute instability growth rate both $dn$ $cn$ background waves considered through stability problem. show that decreases (increases) $dn$-$(cn)$ when vary value modulus parameter.