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A simplified version of Hirota's method for the computation of solitary wavesand solitons of nonlinear PDEs is presented. A change of dependent variabletransforms the PDE into an equation that is homogeneous of degree. Solitons arethen computed using a perturbation-like scheme involving linear and nonlinearoperators in a finite number of steps.  The method is applied to a class of fifth-order KdV equations due to Lax,Sawada-Kotera, and Kaup-Kupershmidt. The method works for non-quadratichomogeneous equations for which the bilinear form might not be known.  Furthermore, homogenization of degree allows one to compute solitary wavesolutions of nonlinear PDEs that do not have solitons. Examples include theFisher and FitzHugh-Nagumo equations, and a combined KdV-Burgers equation. Whenapplied to a wave equation with a cubic source term, one gets a bi-solitonsolution describing the coalescence of two wavefronts. The method is largelyalgorithmic and is implemented in Mathematica.

Symbolic computation of solitary wave solutions and solitons through homogenization of degree