2021/06/28 by A. M. Kamchatnov, D. V. Shaykin · 5 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Classical mechanics #Front (military) #Instability #Mechanics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Nonlinear system #Phase (matter) #Physics #Quantum mechanics #nlin.PS
paper · pdf · open access · doi:10.1209/0295-5075/ac5083
published in Europhysics Letters (EPL) 136(4), 40001 (Institute of Physics) · 7 pages, 2 figures
arxiv created 2021/06/28 · openalex publication_date 2021/11/01 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study evolution of pulses propagating through focusing nonlinear media. Small disturbance on the smooth initial non-uniform background leads to formation of the region of strong nonlinear oscillations. We develop here an asymptotic method for finding the law of motion of the front of this region. The method is applied to the focusing nonlinear Schroedinger equation for the particular cases of Talanov and Akhmanov-Sukhorukov-Khokhlov initial distributions with zero initial phase. The approximate analytical results agree well with the exact numerical solutions for these two problems.