Abstract

ORTIZ ALVAREZ, H. H; JIMENEZ-GARCIA, F. N  and  POSSO AGUDELO, A. E. Some Exact Solutions for a Klein Gordon Equation. ing.cienc. [online]. 2012, vol.8, n.16, pp.57-70. ISSN 1794-9165.

In solving practical problems in science and engineering arises as a direct consequence differential equations that explains the dynamics of the phenomena. Finding exact solutions to this equations provides importan information about the behavior of physical systems. The Lie symmetry method allows to find invariant solutions under certain groups of transformations for differential equations.This method not very well known and used is of great importance in the scientific community. By this approach it was possible to find several exact invariant solutions for the Klein Gordon Equation uxx - utt = k(u). A particular case, The Kolmogorov equation uxx - utt = k₁u + k₂uⁿ was considered. These equations appear in the study of relativistic and quantum physics. The general solutions found, could be used for future explorations on the study for other specific K(u) functions.

Keywords : Lie simmetries; Klein Gordon equation; invariant solutions.

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