2015/08/24 by Mi-Ran Choi, Dirk Hundertmark, Choi, Mi-Ran +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1508.05888
openalex publication_date 2015/08/24 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We prove a threshold phenomenon for the existence of solitary solutions of\nthe dispersion management equation for positive and zero average dispersion for\na large class of nonlinearities. These solutions are found as minimizers of\nnonlinear and nonlocal variational problems which are invariant under a large\nnon-compact group. There exists a threshold such that minimizers exist when the\npower of the solitons is bigger than the threshold. Our proof of existence of\nminimizers is rather direct and avoids the use of Lions' concentration\ncompactness argument. The existence of dispersion managed solitons is shown\nunder very mild conditions on the dispersion profile and the nonlinear\npolarization of optical active medium, which cover all physically relevant\ncases for the dispersion profile and a large class of nonlinear polarizations,\nfor example, they are allowed to change sign.\n