|
|
| |
| The Initial-Boundary-Value Problems for the Hirota Equation on the Half-Line |
| |
Citation： |
Lin HUANG.The Initial-Boundary-Value Problems for the Hirota Equation on the Half-Line[J].Chinese Annals of Mathematics B,2020,41(1):117~132 |
| Page view： 788
Net amount： 660 |
Authors： |
Lin HUANG; |
Foundation： |
This work was supported by the China Postdoctoral
Science Foundation (No.2015M580285). |
|
|
| Abstract： |
An initial boundary-value problem for the Hirota equation on the
half-line, $0 < x < \infty$, $t > 0$, 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 $q(x, 0) = q_0(x)$,
while the remaining spectral functions are defined in terms of the
boundary values $q(0, t) = g_0(t)$, $q_x(0, t) = g_1(t)$ and
$q_{xx}(0, t) = g_2(t)$. The spectral functions satisfy an algebraic
global relation which characterizes, say, $g_2(t)$ in terms of
$\{q_0(x), g_0(t), g_1(t)\}$. The spectral functions are not
independent, but related by a compatibility condition, the so-called
global relation. |
Keywords： |
Hirota equation, Riemann-Hilbert problem, Initial-boundary valueproblem, Global relation |
Classification： |
35Q15, 35Q55 |
|
|
Download PDF Full-Text
|
|
|
|
