The Logarithmic (1+1)-Dimensional KdV-Like and (2+1)-Dimensional KP-Like Equations: Lie Group Analysis, Conservation Laws and Double Reductions

被引：0

作者：

Giresunlu, Ilker Burak ^{[2
]}

Yasar, Emrullah ^{[3
]}

Adem, Abdullahi Rashid ^{[1
]}

机构：

[1] North West Univ, Sch Math & Stat Sci, Mat Sci Innovat & Modelling Focus Area, Private Bag X 2046, ZA-2735 Mmabatho, South Africa

[2] Bilec Seyh Edebali Univ, Fac Arts & Sci, Dept Math, TR-11230 Bilecik, Turkey

[3] Uludag Univ, Fac Arts & Sci, Dept Math, TR-16059 Bursa, Turkey

来源：

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2019年 / 20卷 / 7-8期

关键词：

Lie symmetry group; conservation laws; non-linear self-adjointness; multiplier; generalized double reduction; simplest equation method; NONLINEAR EVOLUTION; SYMMETRIES;

D O I：

暂无

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We investigate the logarithmic (1 + 1) dimensional KdV-like and (2 + 1) dimensional KP-like equations which model many physical processes in the field of soliton theory. In this paper, first, we get the classical Lie point symmetries using the invariance theory. Secondly, we obtain conservation laws of the underlying equations by incorporating the method of multiplier and non-local conservation method. A relationship between the obtained symmetries and conservation laws are shown. Then using the generalized double reduction theory for the associated symmetries, reductions are constructed. Finally traveling wave solutions are computed with the aid of the simplest equation method for the logarithmic (2 + 1)-dimensional KP-like equation.

引用

页码：747 / 755

页数：9

共 18 条

[1]

[Anonymous], 2004, DIRECT METHOD SOLITO

[2]

Bluman G. W., 2010, APPL SYMMETRY METHOD, V168

[3] Generalization of the double reduction theory [J].