Abstract
AbstractWe consider the periodic problem for the Korteweg–de Vries–Burgers (KdVB) equation with pumping where , . We study the solutions, which satisfy the periodic boundary conditions for all and , with the 2π—periodic initial data . Our aim is to find large time asymptotic profile of solutions. The large time asymptotic behavior of solutions to the Cauchy problem for the KdVB equations with different dissipative terms was extensively studied. In the present paper we find the asymptotic profile of solutions for large time. We develop the approach started in Refs. [1, 2, 3]. We prove the following asymptotics for the solutions: as uniformly with respect to , where , , , , , Λ is a constant.
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