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The Hirota Method for reaction-diffusion equations with three distinct roots
Abstract
The Hirota Method, with modified background is applied to construct exact analytical
solutions of nonlinear reaction-diffusion equations of two types. The first equation has only nonlinear
reaction part, while the second one has in addition the nonlinear transport term. For both cases,
the reaction part has the form of the third order polynomial with three distinct roots. We found analytic
one-soliton solutions and the relationships between three simple roots and the wave speed of
the soliton. For the first case, if one of the roots is the mean value of other two roots, the soliton is
static.We show that the restriction on three distinct roots to obtain moving soliton is removed in the
second case by, adding nonlinear transport term to the first equation.