Soliton and breather solutions for the Hirota equation on the elliptic function background

In this paper, we primarily focus our attention on the soliton and breather solutions of a Hirota equation on the backgrounds of elliptic functions such as cn and dn solution backgrounds. Firstly, the solution for the Lax pair of the Hirota equation in the genus-1 case is derived with the algebraic geometry method and subsequently expressed in a unified form with the theta functions. Following that, we deduce the soliton and breather solutions of that equation with the Darboux transformations. Finally, the maximum value of the solutions is derived with the MATLAB's built-in functions.