On the exact solutions, lie symmetry analysis, and conservation laws of Schamel-Korteweg-de Vries equation

2017 ◽  
Vol 40 (11) ◽  
pp. 3927-3936 ◽  
Author(s):  
İ. B. Giresunlu ◽  
Y. Sağlam Özkan ◽  
E. Yaşar
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Vries Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
De Vries

scholarly journals Exact solutions and conservation laws of a coupled integrable dispersionless system

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 957-964 ◽  
Author(s):  
Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Applied Mathematics ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Equation Method ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
Simplest Equation Method ◽  
Mathematics And Physics

In this paper we study the coupled integrable dispersionless system (CIDS), which arises in the analysis of several problems in applied mathematics and physics. Lie symmetry analysis is performed on CIDS and symmetry reductions and exact solutions with the aid of simplest equation method are obtained. In addition, the conservation laws of the CIDS are also derived using the multiplier (and homotopy) approach.

Lie symmetry analysis, exact solutions, conservation laws of variable-coefficients Calogero–Bogoyavlenskii–Schiff equation

2021 ◽  
Author(s):  
Feng Zhang ◽  
Yuru Hu ◽  
Xiangpeng Xin ◽  
Hanze Liu
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Interaction Solution ◽  
Group Invariant Solutions ◽  
Dimensional Variable

In this paper, a [Formula: see text]-dimensional variable-coefficients Calogero–Bogoyavlenskii–Schiff (vcCBS) equation is studied. The infinitesimal generators and symmetry groups are obtained by using the Lie symmetry analysis on vcCBS. The optimal system of one-dimensional subalgebras of vcCBS is computed for determining the group-invariant solutions. On this basis, the vcCBS is reduced to two-dimensional partial differential equations (PDEs) by similarity reductions. Furthermore, the reduced PDEs are solved to obtain the two-soliton interaction solution, the soliton-kink interaction solution and some other exact solutions by the [Formula: see text]-expansion method. Moreover, it is shown that vcCBS is nonlinearly self-adjoint and then its conservation laws are calculated.

scholarly journals Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Expansion Method ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Similarity Reductions

Lie symmetry analysis is performed on a generalized two-dimensional nonlinear Kadomtsev-Petviashvili-modified equal width equation. The symmetries and adjoint representations for this equation are given and an optimal system of one-dimensional subalgebras is derived. The similarity reductions and exact solutions with the aid ofG′/G-expansion method are obtained based on the optimal systems of one-dimensional subalgebras. Finally conservation laws are constructed by using the multiplier method.

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