Direct algebraic method of obtaining exact solutions to nonlinear PDE’s is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model. Special attention is paid to the construction of the kink-like and soliton-like solutions.

Abstract: In this study, we present a numerical scheme to solve the telegraph equation by using Fibonacci polynomials. This method is based on the Fibonacci collocation method which transforms the equation into a matrix equation, and the unknown of this equation is a Fibonacci coefficients matrix. Some numerical examples with comparisons are included to demonstrate the validity and applicabilit...

In this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. By applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. Then, the obtained problems are solved with separation method. In the examples, it is illustrated that the exact solution is ...

In this paper, local and nonlocal symmetry classifications are considered for four equivalent nonlinear telegraph equations. A complete potential symmetry classification of a scalar nonlinear telegraph equation is given through the point symmetry classification of a related potential system. Six new classes of equations are shown to admit potential symmetries. The relationships between local si...

In this paper, we consider a fractional model of telegraph equation in terms of voltage and current. The fractional derivatives are taken in the Caputo sense. The numerical algorithm based on the homotopy perturbation transform method (HPTM) is applied to obtain analytic and approximate solutions of the space-time fractional telegraph equations. The HPTM is combined in the form of Laplace trans...

In this work, q-analogue of the telegraph differential equation is investigated. The approximation solution founded by using Laplace transform collocation method (LTCM). Then, exact compared with for equation. results showed that useful and effective

In this paper we have studied the combination of Elzaki and Laplace transforms to produce a degenerative new double integral transform, transform called Elzaki-Laplace (ELT), then applied it some partial differential equations find its exact solution.