In this paper, we apply Fokas unified method to study the initial boundary value (IBV) problems for nonlinear integrable equation with $3\times 3$ Lax pair on the finite interval $[0,L]$. The solution can be expressed by the solution of a $3\times 3$ Riemann-Hilbert (RH) problem. The relevant jump matrices are written in terms of matrix-value spectral functions $s(k),S(k),S_{l}(k)$, which are determined by initial data at $t=0$, boundary values at $x=0$ and boundary values at $x=L$, respectively. What's more, since the eigenvalues of $3\times 3$ coefficient matrix of $k$ spectral parameter in Lax pair are three different values, search for the path of analytic functions in RH problem becomes a very interesting thing.
Yu XIAO
,
Jian XU
,
Engui FAN
. THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL[J]. Acta mathematica scientia, Series B, 2021
, 41(5)
: 1733
-1748
.
DOI: 10.1007/s10473-021-0520-7
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