Resumen de Rogue Waves on the Periodic Background for the Complex Coupled Integrable Dispersionless Equation

Jian Chang, Zhaqilao Zhaqilao

• This paper investigates rogue wave solutions on the background of the Jacobian elliptic functions for the complex coupled integrable dispersionless equation. Using the travelling wave transformation, we derive Jacobian elliptic function solutions for this equation. Based on the nonlinearization of the Lax pair, we determine the values of the spectral parameters. We construct the linearly independent and non-periodic solutions of the Lax pair with the same spectral parameter. We take the Jacobian elliptic function solutions as the seed solutions, and substitute the linearly independent and non-periodic solutions into the Darboux transformation to obtain the rogue wave solutions on the Jacobian elliptic functions dn and cn backgrounds. The dynamic behaviours and characteristics of these solutions are explored through three-dimensional plots and transverse plots. For both the rogue dn-periodic wave and the rogue cn-periodic wave, when the elliptic modulus k increases, we observe the following distinct changes.

  For the rogue dn-periodic wave, the amplitude of the rogue wave decreases while the amplitude of the periodic background wave increases, and the period becomes larger.

  For the rogue cn-periodic wave, both the amplitude of the rogue wave and that of the periodic background increase, and the period also becomes larger.