Algebraic approaches for deriving soliton solutions and analyzing the stability of coupled Konno-Oono system arising in magnetic field

This article investigates the solutions of the new coupled Konno-Oono system arising in magnetic fields. In this respect, to explore analytical and physical behavior, by applying the two different techniques. The new extended direct algebraic technique and Nucci's direct reduction is used to obtain the different solutions of, new coupled Konno-Oono equation and these soliton type solutions as a singular, mixed singular, periodic, mixed trigonometric, complex combo, trigonometric, mixed hyperbolic, plane, and combined bright-dark soliton. To illustrate the propagation of certain solutions, the graphs associated to these solutions are displayed by selecting suitable parametric values in 3D, 2D as well as contour with the use of the symbolic software {\tt Mathematica}. The visual representation of these findings proves invaluable in grasping the practical significance of the model equation under investigation. The acquired results represent a novel and broader perspective, showcasing the efficacy of the proposed method in analytically addressing nonlinear challenges in mathematical physics and engineering. They offer valuable insights into comprehending magnetic fields, ultimately contributing to the advancement of knowledge in this field. The modulation instability of the model is also discussed. Modulation instability is a versatile and powerful phenomenon of practical applications in scientific research. The computed solutions demonstrate that the methods employed are influential, efficient, and skillful, establishing them as a top choice for addressing non-linear equations in the context of magnetic fields.