Modified Laplace Variational Iteration Method for Analytical Approach of Klein–Gordon and Sine–Gordon Equations

  • Muhammad NadeemEmail author
  • Fengquan Li
Research paper
Part of the following topical collections:
  1. Mathematics


This paper reveals an innovative technique built on variational iteration method and Laplace transformation, called modified Laplace variational iteration method. At first, we apply variational iteration method, and then, Laplace transformation is introduced to calculate the Lagrange multipliers. An innovation of this algorithm shows that Lagrange multiplier has carried out in the absence of integration used in variational iteration method and without taking convolution theorem use in Laplace transform. Furthermore, He’s polynomials are calculated by applying homotopy perturbation method to overcome the nonlinear terms arising in the problems. The proposed method points out that the derived solution exists without any linearization, discretization or any kind of hypothesis. Some numerical models are illustrated which shows the compactness and reliableness of this method.


M-LVIM He’s polynomials Laplace transform Klein–Gordon and Sine–Gordon Equations 



This work is supported by National Natural Science Foundation of China (Grant No: 11571057).


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.School of Mathematical ScienceDalian University of TechnologyDalianChina

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