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Exact solutions to the KdV–Burgers’ equation. (English) Zbl 0833.35124

Summary: This paper presents two different methods for the construction of exact solutions to the KdVB equation. The first is a direct one based on a combination of solutions to the KdV equation and Burgers’ equation. In this approach, a number of unknown constants are involved, and it is shown that the equations leading to their determination are properly determined and are capable of solution. The second method involves a series, and is essentially an extension of Hirota’s method. This approach is capable of solving the KdVB equation exactly, and also of generalization to higher order equations with a KdVB-type nonlinearity.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
35C10 Series solutions to PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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