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The method of simplest equation is applied for obtaining exact solitarytraveling-wave solutions of nonlinear partial differential equations thatcontain monomials of odd and even grade with respect to participatingderivatives. The used simplest equation is $f_\xi^2 = n^2(f^2 -f^{(2n+2)/n})$.The developed methodology is illustrated on two examples of classes ofnonlinear partial differential equations that contain: (i) only monomials ofodd grade with respect to participating derivatives; (ii) only monomials ofeven grade with respect to participating derivatives. The obtained solitarywave solution for the case (i) contains as particular cases the solitary wavesolutions of Korteweg-deVries equation and of a version of the modifiedKorteweg-deVries equation.

Solitary wave solutions of nonlinear partial differential equations based on the simplest equation for the function $1/\cosh^n$