This paper considers the non-linear Kudryashov's equation, that is an extension of well-known dual-power law refractive index and analog to generalized version anti-cubic non-linearity. The model considered in presence full main objective this extract soliton solutions proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, sine-Gordon expansion me...

In this article, a new solution for the (3+1) dimensions Boiti–Leon–Manna–Pempinelli (BLMP) equation using sine Gordon expansion method and extended tanh function is given. The methods were chosen very carefully due to precision of their solutions. Also, some two- three-dimensional figures contours plots obtained solutions presented. Finally, discussion results was

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

In this study, some solitary wave solutions of the Wu-Zhang system are analyzed using modified expansion function method and sine–Gordon method. Solitary non-linear mathematical model consisting hyperbolic trigonometric structures get. Two three dimensional, density graphics models drawn by choosing appropriate parameters. It was seen that all solution functions found as a result provide model....

The perturbation of the Dirac sea to first order in the external potential is calculated in an expansion around the light cone. It is shown that the perturbation consists of a local contribution, which describes the singular behavior of the Dirac sea on the light cone and contains bounded line integrals over the potential and its partial derivatives, and a nonlocal contribution, which is a smoo...

Exploiting the similarities between the Helmholtz wave equation and the Klein-Gordon equation, the former is linearized using the Feschbach-Villars procedure used for linearizing the Klein-Gordon equation. Then the Foldy-Wouthuysen iterative diagonalization technique is applied to obtain a Hamiltonian description for a system with varying refractive index. Besides reproducing all the traditiona...

We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the Hankel transform of order zero. We apply this to give a novel proof, solely based on the causality of this spatio-temporal wave propagation, of th...