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In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein–Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect. By using this method, we obtain abundant new types of exact traveling wave solutions.

turkish journal of physics

Exact traveling wave solutions of the perturbed Klein-Gordon equation with quadratic nonlinearity in (1+1)-dimension, Part I-without local inductance and dissipation effect