## 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.

### MSC:

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

Zbl 0043.09902
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### References:

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