A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutio...A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.展开更多
在这篇论文，我们调查部分微分方程的一个班的能量守恒定律，它联合非线性的电报方程和非线性的散开传送对流方程。而且，联合方程的一些特殊能量守恒定律借助于波浪方程 u <SUB 的对称分类被获得 > x x </SUB>= H (x) u &l...在这篇论文，我们调查部分微分方程的一个班的能量守恒定律，它联合非线性的电报方程和非线性的散开传送对流方程。而且，联合方程的一些特殊能量守恒定律借助于波浪方程 u <SUB 的对称分类被获得 > x x </SUB>= H (x) u <SUB > tt </SUB> 。展开更多
In this paper,by introducing a new transformation,the bilinear form of the coupled integrable dispersionless(CID) equations is derived.It will be shown that this bilinear form is easier to perform the standard Hirota ...In this paper,by introducing a new transformation,the bilinear form of the coupled integrable dispersionless(CID) equations is derived.It will be shown that this bilinear form is easier to perform the standard Hirota process.One-,two-,and three-soliton solutions are presented.Furthermore,the N-soliton solutions are derived.展开更多
A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetrie...A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetries and solutions to Riemann-Hilbert problems in soltion theory.展开更多
文摘A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.
基金National Natural Science Foundation of China under Grant No.10726063
文摘In this paper,by introducing a new transformation,the bilinear form of the coupled integrable dispersionless(CID) equations is derived.It will be shown that this bilinear form is easier to perform the standard Hirota process.One-,two-,and three-soliton solutions are presented.Furthermore,the N-soliton solutions are derived.
基金Supported by the National Natural Science Foundation of China(11975145,11972291)The National Science Foundation(DMS-1664561)。
文摘A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetries and solutions to Riemann-Hilbert problems in soltion theory.
