具有新型扩展mKdV方程的移动边界问题。厄马科夫-皮安内第二类对称性约简的应用
Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlevé II symmetry reduction
AI总结：
本文提出了一种新型扩展mKdV方程，利用厄马科夫-皮安内II类对称性约简，解决斯蒂芬型移动边界问题，并通过反演变换生成可解的移动边界问题类。
摘要：
本文引入了一种新的mKdV方程的扩展形式，该形式允许混合的厄马科夫-皮安内II类对称性约简。将后者应用于获得一类斯蒂芬型移动边界问题的Airy型精确解。然后对后者应用反演变换，以生成一个与基础Casimir成员的紧凑型层次扩展相关的可解的移动边界问题类。证明扩展的mKdV方程被嵌入到一系列具有时间调制的非线性演化方程中，这些方程通过一类源自厄马科夫理论的反演变换确定。对嵌入在经典孤子加纳德方程中的混合mKdV和KdV方程的关联时间调制进行了界定。
英文摘要：
A novel extension of the canonical solitonic mKdV equation is introduced which admits hybrid Ermakov-Painlevé II symmetry reduction. Application of the latter is made to obtain exact solution of Airy-type to a class of moving boundary problems of Stefan kind for this extended mKdV equation. A reciprocal transformation is then applied to the latter to generate an associated exactly solvable class of moving boundary problems for an extension of a base Casimir member of a compacton hierachy. The extended mKdV equation is shown to be embedded in a range of nonlinear evolution equations with temporal modulation as determined via the action of a class of involutory transformations with origin in Ermakov theory. Associated temporal modulation for the hybrid mKdV and KdV equation as embedded in the classical solitonic Gardner equation is delimited.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
