Exact and nonautonomous waves via analytic methods and similarity transformations to fourth-order nonlinear Schrödinger equation
Optik, cilt.353, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 353
- Basım Tarihi: 2026
- Doi Numarası: 10.1016/j.ijleo.2026.172864
- Dergi Adı: Optik
- Derginin Tarandığı İndeksler: Scopus, Compendex, INSPEC, Academic Search Ultimate (EBSCO)
- Anahtar Kelimeler: Exact solutions, Fourth-order nonlinear Schrödinger equation, Nonautonomous solitons, Similarity transformation, Solitary waves
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
We study the fourth-order nonlinear Schrödinger (FONLS) equation that contains higher-order dispersion effects. The equation models ultrashort light pulses in optical fibers. First, we use traveling wave reduction. This turns the partial differential equation into a fourth-order ordinary differential equation. Then we apply the tanh, coth, and sech methods. We find exact solitary wave solutions, including bright and singular solitons, together with their parameter conditions. Next, we work with inhomogeneous media. We develop a new similarity transformation. This transformation connects the constant-coefficient equation to the variable-coefficient equation. It gives nonautonomous solitons. These solitons show how nonlinearity and higher-order dispersion balance each other. This helps in the design of advanced optical systems.