Dynamical features and dispersive soliton solutions of a fractional extended Schrödinger model incorporating cubic-quadratic nonlinear terms

Information from the abstract

This study is devoted to investigating soliton solutions and qualitative analysis of the M-fractional extended nonlinear Schrödinger (NLS) equation with cubicquadratic nonlinear terms. This research is motivated by the significance of the extended NLS model in optics, quantum mechanics, plasma physics, electromagnetic wave propagation, and the approximate description of dense quasione- dimensional Bose–Einstein condensates (BECs) involving repulsive contact interactions and long-range dipole-dipole attraction. The research gap concerns the limited understanding of the combined solitonic, modulational, and dynamical characteristics of this fractional cubic-quadratic model. The novelty lies in integrating the extended rational sine-cosine/sinh-cosh (ERSC–SHC) and generalized exponential rational function (GERFM) methods with modulation instability (MI), sensitivity analysis, bifurcation analysis, and chaos analysis. The contributions include bright, dark, singular, periodic, and exponential soliton structures in single and combined forms, MI regions obtained through linear stability theory, and qualitative analysis supported by graphical representations and phase portraits. A comparative analysis demonstrates distinct dynamical features, providing a foundation for investigations of nonlinear wave propagation and BEC dynamics.

Why this record is monitored

This record has an Impact Signal of 70/100 based on recency, source, collaboration, and bibliographic signals. It prioritizes monitoring and is not a judgment of research quality.

Related topics: Nonlinear Waves and Solitons · Fractional Differential Equations Solutions · Advanced Mathematical Physics Problems