论文标题
在与椭圆曲线相关的耦合kadomtsev- petviashvili系统上
On a coupled Kadomtsev--Petviashvili system associated with an elliptic curve
论文作者
论文摘要
与椭圆曲线相关的耦合的kadomtsev- petviashvili系统，日期提出，Jimbo和Miwa [J.物理。 Soc。 JPn。，52：766--771，1983]在直接线性化框架中进行了重新研究，从一般线性积分方程的角度来看，这为我们提供了对该椭圆模型的整合性的更多见解。结果，我们成功地为椭圆耦合的kadomtsev--petviashvili系统构建了一个不仅由$ 2 \ times 2 $矩阵形式组成的lax对，而且还具有多索矩阵形式，而且还具有带有阶段的阶段，该解决方案由椭圆曲线上的点进行了参数。还讨论了基于直接线性化的尺寸减少，还讨论了椭圆耦合的korteweg-de Vries和Boussinesq系统。此外，对于$ d_ \ infty $ -Type kadomtsev--petviashvili方程，获得了具有非零恒定背景作为副产品的新型解决方案。
The coupled Kadomtsev--Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo and Miwa [J. Phys. Soc. Jpn., 52:766--771, 1983], is reinvestigated within the direct linearisation framework, which provides us with more insights into the integrability of this elliptic model from the perspective of a general linear integral equation. As a result, we successfully construct for the elliptic coupled Kadomtsev--Petviashvili system not only a Lax pair composed of differential operators in $2\times2$ matrix form but also multi-soliton solutions with phases parametrised by points on the elliptic curve. Dimensional reductions based on the direct linearisation, to the elliptic coupled Korteweg-de Vries and Boussinesq systems, are also discussed. In addition, a novel class of solutions are obtained for the $D_\infty$-type Kadomtsev--Petviashvili equation with nonzero constant background as a byproduct.
