论文标题
多孤子解决方案和（2+1）二维变量korteweg-de vries系统的相似性降低
Multiple soliton solutions and similarity reduction of a (2+1)-dimensional variable-coefficient Korteweg-de Vries system
论文作者
论文摘要
在本文中，我们通过其分析溶液研究了（2+1）二维变量korteweg-de Vries（KDV）系统的新型非线性波结构。它的$ n $ - 苏利顿解决方案是通过Hirota的双线性方法获得的，尤其是通过长波极限方法得出的肿块，呼吸和线条溶液的混合溶液。除孤子溶液外，通过对称分析可实现相似性降低，包括相似性解决方案（也称为组不变溶液）和非自治的三阶Painlevé方程。分析结果与说明波相互作用一起显示了有趣的物理特征，这可能会阐明对其他可变的非线性系统的研究。
In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in particular, the hybrid solution of lump, breather and line soliton are derived by the long wave limit method. In addition to soliton solutions, similarity reduction, including similarity solutions (also known as group-invariant solutions) and non-autonomous third-order Painlevé equations, is achieved through symmetry analysis. The analytic results, together with illustrative wave interactions, show interesting physical features, that may shed some light on the study of other variable-coefficient nonlinear systems.
