The Initial-Boundary-Value Problems for the Hirota Equation on the Half-Line

被引：0
作者：
Lin Huang
机构：
[1] Hangzhou Dianzi University,School of Science
[2] Fudan University,School of Mathematical Sciences
来源：
Chinese Annals of Mathematics, Series B | 2020年 / 41卷
关键词：
Hirota equation; Riemann-Hilbert problem; Initial-boundary value problem; Global relation; 35Q15; 35Q55;
D O I：
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学科分类号：
摘要：
An initial boundary-value problem for the Hirota equation on the half-line, 0 < x < ∞, t > 0, is analysed by expressing the solution q(x, t) in terms of the solution of a matrix Riemann-Hilbert (RH) problem in the complex k-plane. This RH problem has explicit (x, t) dependence and it involves certain functions of k referred to as the spectral functions. Some of these functions are defined in terms of the initial condition q(x, 0) = q0(x), while the remaining spectral functions are defined in terms of the boundary values q(0, t) = g0(t), qx(0, t) = g1(t) and qxx(0, t) = g2(t). The spectral functions satisfy an algebraic global relation which characterizes, say, g2(t) in terms of {q0(x), g0(t), g1(t)}. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.
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页码：117 / 132
页数：15
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