Symmetries and Invariant Solutions of Higher-Order Evolution Systems

被引：1

作者：

Tracina, Rita ^{[1
]}

机构：

[1] Univ Catania, Dept Math & Comp Sci, Viale Andrea Doria 6, I-95125 Catania, Italy

来源：

SYMMETRY-BASEL | 2024年 / 16卷 / 08期

关键词：

higher-order evolution systems; Lie symmetries; exact solutions; MODEL;

D O I：

10.3390/sym16081023

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we investigate evolution systems in two components, characterized by higher-order spatial derivatives and the presence of two arbitrary functions. Our study begins with an analysis of a fourth-order system. We perform a detailed group classification and identify specific forms of the constitutive functions that allow the system to exhibit additional symmetries in addition to spatial and temporal translations. We extend these results to nth-order systems. Moreover, we derive invariant solutions for these systems. Finally, for each order n, we are able to find non-negative solutions.

引用

页数：14

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