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- W2006035834 abstract "In this paper, we consider an initial-boundary value problem for the Korteweg-de Vries equation on the positive quarter-plane. The normalised Korteweg-de Vries equation considered is given by where x and τ represent dimensionless distance and time, respectively. In particular, we consider the case when the initial and boundary conditions are given by u(x, 0) = ui for 0 < x < ∞ and u(0, τ) = ub for τ > 0, respectively. Here, the initial value ui > 0 and we restrict attention to values of the boundary value, ub, for which ub < ui. We consider the three cases (ui > 0, ub < 0), (ui > 0, ub = 0) and (ui > 0, 0 < ub < ui). In each case, the method of matched asymptotic coordinate expansions is used to obtain the large-τ asymptotic structure of the solution to this problem, which exhibits the formation of an expansion wave solution." @default.
- W2006035834 created "2016-06-24" @default.
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- W2006035834 date "2010-06-25" @default.
- W2006035834 modified "2023-10-18" @default.
- W2006035834 title "The Large-Time Development of the Solution to an Initial-Boundary Value Problem for the Korteweg-De Vries Equation. II. Expansion Wave Solutions" @default.
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- W2006035834 doi "https://doi.org/10.1093/qjmam/hbq016" @default.
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