The weakly non-linear waves propagation for Kelvin-Helmholtz instability in the magnetohydrodynamics flow impelled by fractional theory.

The weakly nonlinear wave propagation that occurs in the presence of magnetic fields, in which energy is concentrated in a narrow band of wave-numbers in a dispersive and dissipative fluid. The main objective of this paper is to analyze the ( 2 + 1 ) - dimensional elliptic nonlinear Schrodinger equation under the influence of three different fractional operators. The generalized fractional soliton solutions and propagation of magnetohydrodynamics fluid in sort of solition will be visualized. The Conformable, ß and M-truncated fractional operator applied to classical evolution Schrodinger equation. In order to get the analytical closed form solution, one of the generalized approach new extended direct algebraic method is utilized. The fractional nonlinear elliptic Schrodinger equation is developed in three different fractional sense. The similarity transformation technique converted the controlling fractional system to ordinary differential equations. The fractional analytical solutions such as, plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, mixed trigonometric solution, trigonometric solution, shock solution, mixed shock singular solution, mixed singular solution, complex solitary shock solution, singular solution and shock wave solutions are obtained. The graphical 2-D and 3-D representation of the results is shown to express the propagation of fluid with the magnetic field by assuming the appropriate values of the involved parameters. The graphical performance of the obtained solution at various settings of parametric values and fractional order reveals new perspectives and fascinating model phenomena. The attained outcomes have significant applications and have opened up innovative development areas for research across numerous scientific fields.

Analysis of propagating wave structures of the cold bosonic atoms in a zig-zag optical lattice via comparison with two different analytical techniques.

The wave propagation has the significant role in the field of coastal engineering and ocean. In the geographical fields, waves are primary source of environmental process owed to energy conveyance on floating structure. This study aims to investigate the system of cold bosonic atoms in zig-zag optics lattices. The solitonic patterns of the considered model successfully surveyed by using two integrated analytical techniques new extended direct algebraic and G ' G 2 expansion method. The exact solutions are presented by rational, trigonometric, hyperbolic and exponential functions. On the basis of solitons, we need to show that which one is more integrated and robust scheme. These solutions will help to understood the dynamics of cold bosonic atoms in zig-zag optical lattices and the several other systems. Three dimensional as well as two dimensional comparison presented for a cold bosonic atoms model solutions which are revealed diagrammatically for appropriate parameters by using Mathematica. This study will help physicists to predict some new hypothesis and theories in the field of mathematical physics.