Analytical study on the balancing principle for the nonlinear Klein–Gordon equation with a fractional power potential

Abstract

In the literature, although many methods depend on the ansatz solution, there is not any specific rule to determine the degree of the ansatz i.e. balancing principle. The problem is especially seen with the fractional and the generalized nonlinear evolution equations. But the main thing is how many terms are needed to determine explicit solution of these type equations. As the previous work, in this work the balancing principle is generalized for large classes of nonlinear evolution equations, also includes fractional nonlinear models. Keywords: Nonlinear Klein–Gordon Equation with a Fractional Power Potential, BBM equation, Exact solutions