BÄCKLUND TRANSFORMATIONS AND LAX PAIRS FOR THE NONLINEAR KLEIN–GORDON EQUATION WITH SYMBOLIC COMPUTATION

Abstract

In this paper, the nonlinear Klein–Gordon equation describing the propagation of pulse waves in plasma or waveguide is investigated. With symbolic computation, the generalized Bäcklund Transformations (BTs) for this equation are constructed under different conditions. It is shown that the BTs published in the previous literature for the Sine–Gordon equation, Sinh–Gordon equation, and Liouville equation all turn out to be special cases of the results in the present paper. Moreover, the corresponding Lax pairs are explicitly derived from the obtained BTs through some transformations.