Analytical solutions of linear and nonlinear Klein-Fock-Gordon equation

@article{Khan2015AnalyticalSO,
  title={Analytical solutions of linear and nonlinear Klein-Fock-Gordon equation},
  author={Najeeb Alam Khan and Sajida Rasheed},
  journal={Nonlinear Engineering},
  year={2015},
  volume={4},
  pages={43 - 48}
}
Abstract In this paper, we deal with some linear and nonlinear Klein-Fock-Gordon (KFG) equations, which is a relativistic version of the Schrödinger equation. The approximate analytical solutions are obtained by using the homotopy analysis method (HAM). The efficiency of the HAM is that it provides a practical way to control the convergence region of series solutions by introducing an auxiliary parameter }. Analytical results presented are in agreement with the existing results in open… 
5 Citations

Figures from this paper

Numerical analysis of nonlinear fractional Klein–Fock–Gordon equation arising in quantum field theory via Caputo–Fabrizio fractional operator
The present article deals with the solution of nonlinear fractional Klein–Fock–Gordon equation which involved the newly developed Caputo–Fabrizio fractional derivative with non-singular kernel. We
Stable and functional solutions of the Klein-Fock-Gordon equation with nonlinear physical phenomena
The present article uses a modified G′G -expansion method and the generalized Kudryashov method on Klein-Fock-Gordon (KFG) equation and receives some stable and functional solutions. The obtained
Analytical Solutions for Nonlinear Fractional Physical Problems Via Natural Homotopy Perturbation Method
  • A. Arafa
  • Mathematics
    International Journal of Applied and Computational Mathematics
  • 2021
The main objective of this paper is to describe new analytical solutions for the nonlinear fractional Fisher equation, the nonlinear fractional Boussinesq-like equation and the nonlinear fractional

References

SHOWING 1-10 OF 41 REFERENCES
Analytical Study of Navier-Stokes Equation with Fractional Orders Using He's Homotopy Perturbation and Variational Iteration Methods
In the present work, by introducing the fractional derivative in the sense of Caputo, the He's homotopy perturbation method (HPM) and variational iteration method (VIM) are used to study the
An implementation of the ADM for generalized one-dimensional Klein-Gordon equation
  • D. Kaya
  • Mathematics
    Appl. Math. Comput.
  • 2005
Solitons and Nonlinear Wave Equations
A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The
ANALYTICAL ASPECT OF FOURTH-ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS
In this work, the homotopy analysis method (HAM) is applied to solve the fourth-order parabolic partial differential equations. This equation practically arises in the transverse vibration problems.
The variational iteration method for studying the Klein-Gordon equation
...
...