论文标题
半线上线性化的古典Boussinesq系统
The Linearized Classical Boussinesq System on the Half-Line
论文作者
论文摘要
在半行的非零边界条件的情况下，经典Boussinesq系统的线性化被明确求解。该分析依赖于FOKA的统一变换方法，并在两个不同的框架中进行：（i）通过利用最近引入的FOKAS的方法扩展到方程式系统； （ii）通过将线性化的经典boussinesq系统表示为单个高阶方程，然后通过统一变换的通常版本求解。所得公式为半线上线性化的经典BoussinesQ系统提供了一种新颖的表示。此外，由于边界处的均匀收敛性，新型公式被证明可以满足线性化的古典Boussinesq系统以及通过直接计算的规定初始和边界数据。
The linearization of the classical Boussinesq system is solved explicitly in the case of nonzero boundary conditions on the half-line. The analysis relies on the unified transform method of Fokas and is performed in two different frameworks: (i) by exploiting the recently introduced extension of Fokas's method to systems of equations; (ii) by expressing the linearized classical Boussinesq system as a single, higher-order equation which is then solved via the usual version of the unified transform. The resulting formula provides a novel representation for the solution of the linearized classical Boussinesq system on the half-line. Moreover, thanks to the uniform convergence at the boundary, the novel formula is shown to satisfy the linearized classical Boussinesq system as well as the prescribed initial and boundary data via a direct calculation.
