Explicit solitary wave solutions for the nonlinear equations in semiconductor and magnetic field with their stability analysis

In this manuscript, the Sobolev-type equations are examined analytically. The Sobolev-type equations are important in many fields, including thermodynamics, physics, soil mechanics, fluid flow through fissured rock sand, shear in second-order fluids, and mechanical engineering. We have looked into two dynamical systems involving Sobolev type nonlinear equations with magnetic field and semi-conductor applications. Numerous sorts of solutions have been successfully obtained using the new modified extended direct algebraic method. In addition to single and mixed wave structures, shock, shock-singular, complex solitary-shock, and periodic-singular forms can be found in the extracted solutions. Both models' linear stability analyses are discussed, and conditions are created. The graphical behaviour of the state variable is displayed in 3D, line graph, and the corresponding contours are shown for a range of parameter values. Mathematica software is used for calculations and to draw physical behavior.