@article{Amplitude modulation of three-dimensional low-frequency solitary waves in a magnetized dusty superthermal plasma_2023, volume={11}, url={https://oiccpress.com/journal-of-theoretical-and-applied-physics/article/amplitude-modulation-of-three-dimensional-low-frequency-solitary-waves-in-a-magnetized-dusty-superthermal-plasma/}, DOI={10.1007/s40094-017-0255-y}, abstractNote={AbstractThe amplitude modulation of three-dimensional (3D) dust ion-acoustic wave (DIAW) packets is studied in a collisionless magnetized plasma with inertial positive ions, superthermal electrons and negatively charged immobile dust grains. By using the reductive perturbation technique, a 3D-nonlinear Schrödinger equation is derived, which governs the slow modulation of DIAW packets. The latter are found to be stable in the low-frequency (ωomega _{ ext {c }$$end{document}, and the modulational instability is related to the modulational obliqueness (θ)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$( heta )$$end{document}. Here, ω(ωc)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$omega ~(omega _{ ext {c })$$end{document} is the nondimensional wave (ion-cyclotron) frequency. It is shown that the superthermal parameter κdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$kappa$$end{document}, the frequency ωcdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$omega _{ ext {c }$$end{document} as well as the charged dust impurity (0}, number={3}, journal={Journal of Theoretical and Applied Physics}, publisher={OICC Press}, year={2023}, month={Nov.}, keywords={NLS equation, Modulational instability, Superthermal plasma, Dusty plasma, Solitary wave} }