https://doi.org/10.1140/epjp/s13360-021-01190-9
Regular Article
Rogue waves on the double-periodic background in Hirota equation
Department of Nonlinear Dynamics, Bharathidasan University, 620024, Tiruchirappalli, Tamil Nadu, India
Received:
18
September
2020
Accepted:
3
February
2021
Published online:
10
March
2021
We construct rogue wave solutions on the double-periodic background for the Hirota equation through onefold Darboux transformation formula. We consider two types of double-periodic solutions as seed solutions. We identify the squared eigenfunctions and eigenvalues that appear in the onefold Darboux transformation formula through an algebraic method with two eigenvalues. We then construct the desired solution in two steps. In the first step, we create double-periodic waves as the background. In the second step, we build rogue wave solution on the top of this double-periodic solution. We present the localized structures for two different values of the arbitrary parameter each one with two different sets of eigenvalues.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
