
 
The InitialBoundaryValue Problems for the Hirota Equation on the HalfLine 
 
Citation： 
Lin HUANG.The InitialBoundaryValue Problems for the Hirota Equation on the HalfLine[J].Chinese Annals of Mathematics B,2020,41(1):117~132 
Page view： 115
Net amount： 114 
Authors： 
Lin HUANG; 
Foundation： 
This work was supported by the China Postdoctoral
Science Foundation (No.2015M580285). 


Abstract： 
An initial boundaryvalue problem for the Hirota equation on the
halfline, $0 < x < \infty$, $t > 0$, is analysed by expressing the
solution $q(x, t)$ in terms of the solution of a matrix
RiemannHilbert (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 socalled
global relation. 
Keywords： 
Hirota equation, RiemannHilbert problem, Initialboundary valueproblem, Global relation 
Classification： 
35Q15, 35Q55 

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