Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation
Wen-Xiu Ma, Benno Fuchssteiner
Abstract
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ansätze. 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. Bäcklund transformations of the linear form and some special cases are considered.
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