Double Sumudu Transform Iterative Method for One-Dimensional Nonlinear Coupled Sine-Gordon Equation

In this paper, the combined double Sumudu transform with iterative method is successfully implemented to obtain the approximate analytical solution of the one-dimensional coupled nonlinear sine-Gordon equation (NLSGE) subject to the appropriate initial and boundary conditions which cannot be solved by applying double Sumudu transform only. The solution of the nonlinear part of this equation was solved by a successive iterative method, the proposed technique has the advantage of producing an exact solution, and it is easily applied to the given problems analytically. Two test problems from mathematical physics were taken to show the liability, accuracy, convergence, and efficiency of the proposed method. Furthermore, the results indicate that the introduced method is promising for solving other types of systems of NLPDEs.

New Optical Solitons And Modulation Instability Analysis of Generalized Coupled Nonlinear Schrodinger-KdV System

In this study, the generalized coupled nonlinear Schrodinger-KdV (NLS-KdV) system is investigated to obtain new optical soliton solutions. This system appears as a model for reciprocity between long and short waves in various of physical settings. Different kind of new soliton solutions including dark, bright, combined dark-bright, singular and combined singular soliton solutions are obtained using two effective methods namely, the extended sinh-Gordon equation expansion method and the solitary wave ansatz method. In addition, the modulation instability analysis of the system is presented based on the standard linearstability analysis. The behaviours of obtained solutions are expressed by 3D graphs.

New Solution of the Sine-Gordon Equation by the Daftardar-Gejji and Jafari Method

In this article, the Daftardar-Gejji and Jafari method (DJM) is used to obtain an approximate analytical solution of the sine-Gordon equation. Some examples are solved to demonstrate the accuracy of DJM. A comparison study between DJM, the variational iteration method (VIM), and the exact solution are presented. The comparison of the present symmetrical results with the existing literature is satisfactory.

Analysis of nonlinear time-fractional Klein-Gordon equation with power law kernel

<abstract><p>We investigate the nonlinear Klein-Gordon equation with Caputo fractional derivative. The general series solution of the system is derived by using the composition of the double Laplace transform with the decomposition method. It is noted that the obtained solution converges to the exact solution of the model. The existence of the model in the presence of Caputo fractional derivative is performed. The validity and precision of the presented method are exhibited with particular examples with suitable subsidiary conditions, where good agreements are obtained. The error analysis and its corresponding surface plots are presented for each example. From the numerical solutions, we observe that the proposed system admits soliton solutions. It is noticed that the amplitude of the wave solution increases with deviations in time, that concludes the factor $ \omega $ considerably increases the amplitude and disrupts the dispersion/nonlinearity properties, as a result, may admit the excitation in the dynamical system. We have also depicted the physical behavior that states the advancement of localized mode excitations in the system.</p></abstract>

Stationary multi-kinks in the discrete sine-Gordon equation

We consider the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a representative example of the family of discrete Klein–Gordon models. The multi-kinks are constructed using Lin’s method from an alternating sequence of well-separated kink and antikink solutions. We then locate the point spectrum associated with these multi-kink solutions by reducing the spectral problem to a matrix equation. For an m-structure multi-kink, there will be m eigenvalues in the point spectrum near each eigenvalue of the primary kink, and, as long as the spectrum of the primary kink is imaginary, the spectrum of the multi-kink will be as well. We obtain analytic expressions for the eigenvalues of a multi-kink in terms of the eigenvalues and corresponding eigenfunctions of the primary kink, and these are in very good agreement with numerical results. We also perform numerical time-stepping experiments on perturbations of multi-kinks, and the outcomes of these simulations are interpreted using the spectral results.

Dirac Equation in Cosmological Inertial Frame

Dirac equation is a one order-wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Dirac Equation from wave function, Type A in cosmological inertial frame.The Dirac equation satisfy Klein-Gordon equation in cosmological inertial frame.

Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

Klein-Gordon Equation and Wave Function for Free Particle in Rindler Space-Time

Klein-Gordon equation is a relativistic wave equation. It treats spinless particle. The wave functioncannot use as a probability amplitude. We made Klein-Gordon equation in Rindler space-time. In this paper,we make free particle’s wave function as the solution of Klein-Gordon equation in Rindler space-time.