Физико-математические науки
Exact Solitary-wave Solution of the Generalized Gardner-Burgers Equation
Zemlyanukhin A.I. 2, Bochkarev A.V. 1
1. Yuri Gagarin state technical university of Saratov 2. Yuri Gagarin state technical university of Saratov
Abstract:
A direct perturbation method is applied for finding exact solitary-wave solution to the Gardner-Burgers equation. Using a perturbation series the connection of the Gardner-Burgers equation with a pair of Riccati equations is established. It is shown that the exact solution can be obtained from the Cole-Hopf transformation that contains the function, which is the solution of a second-order differential equation with constant coefficients. An exact solution of the generalized Gardner-Burgers equation with fourth-order polynomial in the dependent variable is found.
Keywords: exact solitary-wave solutions, perturbation method, Riccati equation
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