On the orbital stability of solitary waves for the fourth order nonlinear Schr\"odinger equation

• DOI: 10.48550/arxiv.2405.09268
• Publication Date: 2024-05-15
• Authors: Handan Borluk; Gülçin M. Muslu; Fábio Natali
• Keywords: FOS: Mathematics; Analysis of PDEs (math.AP)

In this paper, we present new results regarding the orbital stability of solitary standing waves for general fourth-order Schr\"odinger equation with mixed dispersion. The existence can be determined both as minimizers a constrained complex functional and by using numerical approach. addition, specific values frequency associated wave, one obtains explicit solutions hyperbolic secant profile. Despite these being functional, they cannot seen smooth curve waves, fact prevents their determination classical approaches in current literature. To overcome difficulty, employ approach to construct waves. is useful showing threshold power $\alpha_0\approx 4.8$ nonlinear term such that if $\alpha\in (0,\alpha_0),$ wave stable, $\alpha>\alpha_0$, unstable. An important feature our work, caused presence dispersion term, concerns value $\alpha_0 \approx not same established proving global energy space, well known equation.