Operational Solution to the Nonlinear Klein-Gordon Equation

Abstract

We obtain solutions of the nonlinear Klein-Gordon equation using a novel algebraic operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions.

Stable and functional solutions of the Klein-Fock-Gordon equation with nonlinear physical phenomena

“…-expansion method [9,10], novel (G′/G)-expansion method [11,12], nonlinear adaptive control scheme [13], the unified method and its generalized form [14][15][16][17], Linear non-adaptive boundary control law [18,19], the improved Bernoulli sub-equation function method [20], tanh-coth expansion method [21], rational sine-cosine method [22], the sine-Gordon expansion method [23,24], the enhanced modified simple equation method [25], the exponential rational function method [26], the simplified Hirotas method [27], Darboux transformation method [28], N-fold Darboux transformation [29], Lie symmetry approach [30], the power index method [31], generalized Kudryashov method [32], novel operational method [33], extended simple equation [34], (G′/G)-expansion method [35], the extended sinh-Gordon equation expansion method [36,37], the Hirota bilinear approach [38,39], the extended rational sinecosine and rational sinh-cosh methods [40], new extended rational SGEE method [41], the extended unified method [42,43] and many other approaches.…”