Symmetry reductions, group-invariant solutions and conservation laws of a three-coupled Korteweg-de Vries system

2019 ◽  
Vol 60 ◽  
pp. 665-675
Author(s):  
Xia-Xia Du ◽  
Bo Tian ◽  
Yu-Qiang Yuan ◽  
Chen-Rong Zhang ◽  
Zhong Du
Keyword(s):  
Conservation Laws ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Symmetry Reductions ◽  
De Vries ◽  
Group Invariant Solutions

Exact Group Invariant Solutions and Conservation Laws of the Complex Modified Korteweg–de Vries Equation

2013 ◽  
Vol 68 (8-9) ◽  
pp. 510-514 ◽  
Author(s):  
Andrew G. Johnpillai ◽  
Abdul H. Kara ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Symmetry Algebra ◽  
Lie Symmetry ◽  
Point Of View ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Symmetry Approach ◽  
De Vries ◽  
Group Invariant Solutions ◽  
Symmetry Generators

We study the scalar complex modified Korteweg-de Vries (cmKdV) equation by analyzing a system of partial differential equations (PDEs) from the Lie symmetry point of view. These systems of PDEs are obtained by decomposing the underlying cmKdV equation into real and imaginary components. We derive the Lie point symmetry generators of the system of PDEs and classify them to get the optimal system of one-dimensional subalgebras of the Lie symmetry algebra of the system of PDEs. These subalgebras are then used to construct a number of symmetry reductions and exact group invariant solutions to the system of PDEs. Finally, using the Lie symmetry approach, a couple of new conservation laws are constructed. Subsequently, respective conserved quantities from their respective conserved densities are computed.

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