# 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…

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## 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

- Mathematics
- 2009

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

- MathematicsAppl. Math. Comput.
- 2005

Differential transform method for solving the linear and nonlinear Klein-Gordon equation

- Mathematics, PhysicsComput. Phys. Commun.
- 2009

Solitons and Nonlinear Wave Equations

- Physics, Mathematics
- 1982

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

- Mathematics
- 2010

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

- Mathematics, PhysicsAppl. Math. Lett.
- 2008

Variational principles for some nonlinear partial differential equations with variable coefficients

- Mathematics
- 2004

THE APPLICATION OF HOMOTOPY ANALYSIS METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER

- Mathematics, Physics
- 2006