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

更新时间:2023-05-28

【摘要】An initial boundary-value problem for the Hirota equation on the half-line,00, 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.

【关键词】

阅读全文