2022/08/03 by N. Sinthuja, Sinthuja, N., S. Rajasekar +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Gyrotron and Vacuum Electronics Research #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2208.01878
openalex publication_date 2022/08/03 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We compute the instability rate for single- and double-periodic wave solutions of a fourth-order nonlinear Schrödinger equation. The single- and double-periodic solutions of a fourth-order nonlinear Schrödinger equation are derived in terms of Jacobian elliptic functions such as dn, cn, and sn. From the spectral problem, we compute Lax and stability spectrum of single-periodic waves. We then calculate the instability rate of single-periodic waves (periodic in the spatial variable). We also obtain the Lax and stability spectrum of double-periodic wave solutions for different values of the elliptic modulus parameter. We also highlight certain novel features exhibited by the considered system. We then compute instability rate for two families of double-periodic wave solutions of the considered equation for different values of the system parameter. Our results reveal that the instability growth rate is higher for the double-periodic waves due to the fourth-order dispersion parameter when compared to single-periodic waves.