Reductions and conservation laws for BBM and modified BBM equations

被引：3

作者：

Khorshidi, Maryam ^{[1
]}

Nadjafikhah, Mehdi ^{[2
]}

Jafari, Hossein ^{[3
,4
]}

Al Qurashi, Maysaa ^{[5
]}

机构：

[1] Firuzabad Inst Higher Educ, POB 74717-94469, Firuzabad, Fars, Iran

[2] Iran Univ Sci & Technol, Sch Math, Dept Pure Math, Tehran 1684613114, Iran

[3] Univ Mazandaran, Dept Math, Babol Sar, Iran

[4] Univ South Africa, Dept Math Sci, POB 392, ZA-0003 Unisa, South Africa

[5] King Saud Univ, Dept Math, Riyadh 11495, Saudi Arabia

来源：

OPEN MATHEMATICS | 2016年 / 14卷

关键词：

Lie symmetries; Group-invariant solutions; Optimal system of Lie sub-algebras; Conservation laws; BBM and MBBM equations;

D O I：

10.1515/math-2016-0101

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.

引用

页码：1138 / 1148

页数：11

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