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We develop two new equations which describe propagation of two different wave modes simultaneously. The first equation is a two-mode Sharma-Tasso-Olver equation, and the second is a two-mode fourth-order Burgers equation. We show that multiple kink solutions for each model exist only for specific values of the nonlinearity and dispersion parameters included in the models. We will use the Cole-Hopf transformation combined with the simplified Hirota’s method to conduct this analysis. Keywords: Two-mode equations, Dispersion relation, Multiple kink solutions