This paper is concerned with investigating the spatial decay estimates for linear demped Hyperbolic equations in the space-time region Ώ×(0,∞) where Ώ is the semi-infinite prismatic cylinder.

This article studies a complex Hyperbolic Schrodinger dynamical equation that is associated with nonlinear media via ultra short pulse propagation. The modified simplest equation method is executed to construct complex solitary wave and other solutions of the aforesaid equation by considering it in conformable M-fractional derivative sense. The acquired solutions are in the form of solitary and periodic waves and rational functions. These solutions are also described with their graphical representations by assuming appropriate values of required parameters. Moreover, the results show that the aforesaid approach can be effective for solving such nonlinear Schrodinger equations arising in nonlinear optics and physical sciences.

In this paper, we study the blow-up of solutions for Hyperbolic equations involving the fractional Laplacian operator with damping and source terms.  We obtain the global existence results. Then, we observe the blow-up of solutions using the concavity method. Finally, we present some numerical simulation results.

By constructing a newly modified cubic B-splines having the optimal accuracy order four, we propose a numerical scheme for solving the Hyperbolic telegraph equation using a differential quadrature method. The spatial derivatives are approximated by the differential quadrature whose weight coefficients are computed using the newly modified cubic B-splines. Our modified cubic B-splines retain the tridiagonal structure and achieve the fourth order convergence rate. The solution of the associated ODEs is advanced in the time domain by the SSPRK scheme. The stability of the method is analyzed using the discretization matrix. Our numerical experiments demonstrate the better performance of our proposed scheme over several known numerical schemes reported in the literature.

In this work, an initial-boundary value problem with a non-classic condition for the one-dimensional wave equation is presented and the reduced differential transform method is applied to ascertain the solution of the problem. We will investigate a new kind of non-local boundary value equations in which are the solution of Hyperbolic partial differential equations with a non-standard boundary characteristic. The advantage of this method is its simplicity in using, it solves the problem directly and straightforward without using perturbation, linearization, Adomian’ s polynomial or any other transformation and gives the solution in the form of convergent power series with simply determinable components. Also, the convergence of the method is proved and seven examples are tested to shows the competency of our study.

The wave equations are one of the most important equations in engineering and physics, which are usually formulated as Hyperbolic partial differential equations with special boundary conditions. In this paper, a numerical method for solving these equations based on Bernstein polynomials is introduced. The properties of Bernstein polynomial operational matrices turn this differential equation and its boundary conditions into a system of algebraic equations. Some numerical examples illustrate the accuracy, validity, and applicability of the new technique.

The current study utilizes the extended sinh-Gordon equation expansion and ( G'/G2)-expansion function methods in constructing various optical soliton and other solutions to the (2+1)-dimensional Hyperbolic nonlinear Schrodinger’, s equation which describes the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics. We secure different kinds of solutions like optical dark, bright, singular, combo solitons as well as Hyperbolic and trigonometric functions solutions. Moreover, singular periodic wave solutions are recovered and the constraint conditions which provide the guarantee to the soliton solutions are also reported. In order to shed more light on these novel solutions, graphical features 3D, 2D and contour with some suitable choice of parameter values have been depicted. We also discuss the stability analysis of the studied nonlinear model with aid of modulation instability analysis.