Exact solutions of the Burgers-Huxley equation. (Russian, English) Zbl 1092.35084

Prikl. Mat. Mekh. 68, No. 3, 462-469 (2004); translation in J. Appl. Math. Mech. 68, No. 3, 413-420 (2004).
The authors study the Burgers-Huxley equation \[ U_t+\alpha UU_x = DU_{xx}+\beta U+\gamma U2 - \delta U3,\quad d\neq 0\tag{1} \] which describes some nonlinear wave effects. By means of the Cole-Hopf substitution [J. D. Cole, Q. Appl. Math. 9, No. 3, 225–236 (1951; Zbl 0043.09902)] an exact solution to equation (1) is obtained. The types of exact solution are analysed depending on the parameter values of the equation.


35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q51 Soliton equations


Zbl 0043.09902
Full Text: DOI


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