Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation

Details Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation

1995-11-14

arxiv.org/abs/solv-int/9511005v3

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14pages, Latex, to appear in Intern. J. Nonlinear Mechanics, the original latex file is not complete

Scientific paper

10.1016/0020-7462(95)00064-X

Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\"acklund transformations of the linear form and some special cases are considered.

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