Dynamics of soliton solutions in saturated ferromagnetic materials by a novel mathematical method

• Published in: Journal of magnetism and magnetic materials 2021-11, Vol.538, p.168245, Article 168245
• Main Authors: Shafqat-Ur-Rehman, Bilal, Muhammad, Ahmad, Jamshad
• Format: Article
• Language: English
• Subjects: Ferromagnetic materials; Kraenkel-Manna-Merle system; Mathematical analysis; New extended direct algebraic method; Nonlinear differential equations; Parameters; Partial differential equations; Plane waves; Saturated ferromagnetic material; Solitary waves; Soliton solutions
• ISSN: 0304-8853; 1873-4766
• DOI: 10.1016/j.jmmm.2021.168245

•The (1 + 1)-dimensional Kraenkel-Manna-Merle system is studied.•A new extended direct algebraic method is employed.•Hyperbolic, dark, singular, periodic and combined soliton solutions are extracted.•Moreover, 3D, 2D and contour graphs of some reported solutions have been depicted. In this research work, we retrieve dynamics of new soliton solutions to the Kraenkel-Manna-Merle system which describes the nonlinear ultrashort pulse in saturated ferromagnetic materials having an external field with zero-conductivity by utilizing the new extended direct algebraic method. The soliton and other solutions achieved by this method can be categorized as a single (dark, singular), complex combo solitons as well as complex hyperbolic, plane wave and trigonometric solutions with arbitrary parameters. The spectrum of solitons is enumerated along with their existence criteria. Moreover, 2-D, 3-D, and their contour profiles of reported results are also sketched by substituting the diverse values to the parameters that facilitate the researchers to comprehend the physical phenomena of the governing equation. The results reveal the system theoretically possesses extremely rich soliton structures. The acquired solutions exhibit that the proposed technique is an efficient, valuable, and straightforward approach to constructing new solutions of various types of nonlinear partial differential equations which have important applications to applied sciences and engineering.