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

共 50 条

[31] 组合BBM与修正BBM方程的精确解
尚亚东
纺织高校基础科学学报, 1998, (02) : 46 - 50
[32] Attractors for the Ginzburg-Landau-BBM equations in an unbounded domain
Inst. Appl. Phys. and Compl. Math., Beijing 100088, China
不详
不详
Communications in Nonlinear Science and Numerical Simulation, 1998, 3 (02): : 78 - 82
[33] On Galilean Invariant and Energy Preserving BBM-Type Equations
Cheviakov, Alexei
Dutykh, Denys
Assylbekuly, Aidar
SYMMETRY-BASEL, 2021, 13 (05):
[34] Asymptotic Stablity of Global Solutions for Some Nonlinear BBM Equations
YE, Yaojun
INTERNATIONAL CONFERENCE ON APPLIED PHYSICS AND INDUSTRIAL ENGINEERING 2012, PT C, 2012, 24 : 2279 - 2285
[35] ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN
郭柏灵
蒋慕蓉
ActaMathematicaScientia, 2000, (01) : 122 - 130
[36] Stability properties of solitary waves for fractional KdV and BBM equations
Pava, Jaime Angulo
NONLINEARITY, 2018, 31 (03) : 920 - 956
[37] Wave Turbulence for the BBM Equation: Stability of a Gaussian Statistics Under the Flow of BBM
de Suzzoni, Anne-Sophie
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 326 (03) : 773 - 813
[38] Study of W-shaped, V-shaped, and other type of surfaces of the ZK-BBM and GZD-BBM equations
Kayum, Md. Abdul
Roy, Ripan
Akbar, M. Ali
Osman, M. S.
OPTICAL AND QUANTUM ELECTRONICS, 2021, 53 (07)
[39] BBM-928, A NEW ANTI-TUMOR ANTIBIOTIC COMPLEX .3. STRUCTURE DETERMINATION OF BBM-928-A, BBM-928-B AND BBM-928-C
KONISHI, M
OHKUMA, H
SAKAI, F
TSUNO, T
KOSHIYAMA, H
NAITO, T
KAWAGUCHI, H
JOURNAL OF ANTIBIOTICS, 1981, 34 (02): : 148 - 159
[40] Study of W-shaped, V-shaped, and other type of surfaces of the ZK-BBM and GZD-BBM equations
Md. Abdul Kayum
Ripan Roy
M. Ali Akbar
M. S. Osman
Optical and Quantum Electronics, 2021, 53

← 1 2 3 4 5 →