Solving One-Dimensional Non-Linear Klein-Gordon Equations via Combining Adomian Polynomials and Rohit Transform Method

In this study, one-dimensional non-linear Klein-Gordon equations are solved by applying the integral transform known as the Rohit transform method. The approximate solutions of one-dimensional non-linear Klein- Gordon equations are obtained by combining the Adomian polynomials with the Rohit transform. To show the effectiveness and performance of the Rohit transform method, five one-dimensional non-linear Klein- Gordon type equations are considered and solved. The graphs of the solutions obtained are plotted to indicate the generality and clarity of the proposed method. It can be easily verified that the proposed method yielded the results that satisfy their corresponding non-linear Klein-Gordon equations. The integral Rohit transform combined with Adomian polynomials brought progressive methodologies that offer new insights on the problems (i.e., one-dimensional non-linear Klein-Gordon) examined in the paper, distinguishing itself from existing methods and doubtlessly beginning up new research instructions. Moreover, it reduces the complexity that occurs when non-linear Klein-Gordon are solved by other methods available in the literature. It provided precise results for the specific problems discussed in the paper, surpassing the capabilities of different methods in terms of decision, constancy, or robustness to noise and disturbances.