2020/08/27 by N. Sinthuja, K. Manikandan, Sinthuja, N. +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2008.12116
openalex publication_date 2020/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct rogue wave solutions on the double periodic background for the Hirota equation through one fold 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 one fold 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.