Abstract As Davey–Stewartson system is considered one of the most important models in optics, quantum physics, plasmas, and Bose–Einstein condensates. In this study, we have solved the Davey–Stewartson system using a modified Jacobi elliptic function methodology, and therefore many novel Jacobi elliptic wave function solutions were obtained, which degenerated to hypergeometric functions and periodic functions. The results obtained in this paper are novel in addition, contain other results achieved before in literatures. Moreover, some dynamic behavior for the periodic, kink type, and soliton wave propagation is demonstrated.
The propagation of a cylindrical shock wave in rotating medium with azimuthal magnetic field under the action of monochromatic radiation using a method of group invariance is investigated. To derive similarity solutions as well as exact solutions, the group invariance technique is used. All classes of the solutions depending on the absorption coefficient are discussed by considering absorption coefficient to be variable or constant. A similarity solution is obtained, when the absorption coefficient is assumed to be variable. Two cases of solutions with a power law shock path are obtained by the different choices of arbitrary constants involving in the infinitesimal generators of the Lie group of transformations. To obtain the similarity solution in the case of the power law shock path, the density, magnetic field, axial and azimuthal velocity components are assumed to be varying and obeying power laws in the undisturbed medium. It is observed that with increase in the values of Alfven Mach number, adiabatic exponent and rotational parameter, shock strength decreases. The effects of variation of magnetic field strength, adiabatic exponent, rotational parameter and initial magnetic field variation index on the flow variables and on shock waves are analyzed graphically. Also, all classes of exact solutions are obtained by considering a constant absorption coefficient.
Abstract This paper generates a novel approach called the clique polynomial method (CPM) using the clique polynomials raised in graph theory and used for solving the fractional order PDE. The fractional derivative is defined in terms of the Caputo fractional sense and the fractional partial differential equations (FPDE) are converted into nonlinear algebraic equations and collocated with suitable grid points in the current approach. The convergence analysis for the proposed scheme is constructed and the technique proved to be uniformly convegant. We applied the method for solving four problems to justify the proposed technique. Tables and graphs reveal that this new approach yield better results. Some theorems are discussed with proof.
Abstract In this paper, a class of strictly hyperbolic systems of conservation laws which arises in connection with enhanced oil recovery is studied. The Riemann problem is solved analytically. The Riemann solutions with two kinds of different structures involving the delta-shock are obtained. For delta-shock, the generalized Rankine–Hugoniot relations and over-compressive delta-entropy condition are clarified. Further, the existence and uniqueness of delta-shock are established. The theoretical analysis is tested accurately by the numerical results.
Abstract The generation of clean energy from wind has recently received huge attention. Thanks to the current advances of adaptive algorithms due to their benefits and flexibility. The paper introduces a new smart radial basis function (RBF) neural network to extract the optimal energy from wind for wind energy conversion systems. This scheme uses the electrical energy of the doubly fed induction-generator (DFIG) as an input in wind turbines drives a DFIG to acquire maximum energy from the available wind under uncertainties and fast-changing wind conditions. Thus, to prove the quality of our proposed intelligent scheme, a comparative study with conventional optimum power is applied to a wind turbine driving a class of 1.5 MW DFIG during the transient operation. Furthermore, the analysis and the interpretation of raw and processed real measured data using the process of linear interpolation through Matlab/Simulink illustrate the relevance and the performance of the sensorless controller for the overall wind turbine system. Briefly, the numerical simulation studies show that a good efficiency and improved tracking of the smart RBF-neural network controller when implemented online below the real wind speed despite the unknown parameters.
