Vector shock soliton and the Hirota bilinear method. (English) Zbl 1070.35056

From the summary: The Hirota bilinear method is applied to find an exact shock soliton solution to a system of reaction-diffusion equations \[ \frac {\partial u}{\partial t}= \nabla^2u- (u-a_1)(u-a_2)(u-a_3) \] for the \(n\)-component vector order parameter \(u\), with the reaction part in form of a third-order polynomial, determined by three distinct constant vectors.


35Q51 Soliton equations
37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations
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