scholarly journals Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion

2020 ◽  
Vol 13 (10) ◽  
pp. 2691-2701
Author(s):  
María-Santos Bruzón ◽  
◽  
Elena Recio ◽  
Tamara-María Garrido ◽  
Rafael de la Rosa
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Lie Symmetries

scholarly journals Lie Symmetries, Conservation Laws and Exact Solutions for Jaulent-Miodek Equations

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1319
Author(s):  
Jian-Ting Pei ◽  
Yu-Shan Bai
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Algebra ◽  
Adjoint Equation ◽  
Lie Symmetries ◽  
Equation Method ◽  
One Dimensional

In this paper, the Lie symmetries of the Jaulent-Miodek (JM) equations are calculated and one dimensional optimal systems of Lie algebra are obtained. Furthermore, the conservation laws are constructed by using the adjoint equation method. Finally, the exact solutions of the equations are obtained by the conservation laws.

scholarly journals On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
P. Masemola ◽  
A. H. Kara
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Schrodinger Equation ◽  
Lie Symmetries ◽  
Pt Symmetry ◽  
Noether Symmetries ◽  
Cubic Schrödinger Equation ◽  
The Relationship

An analysis of a PT symmetric coupler with “gain in one waveguide and loss in another” is made; a transformation in the PT system and some assumptions results in a scalar cubic Schrödinger equation. We investigate the relationship between the conservation laws and Lie symmetries and investigate a Lagrangian, corresponding Noether symmetries, conserved vectors, and exact solutions via “double reductions.”

Symmetries and conservation laws of a damped Boussinesq equation

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640012 ◽  
Author(s):  
María Luz Gandarias ◽  
María Rosa
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Source Term ◽  
Boussinesq Equation ◽  
Lie Symmetries ◽  
Multiplier Method ◽  
Independent Source ◽  
Damped Equation

In this work, we consider a damped equation with a time-independent source term. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. We also present some exact solutions. Conservation laws for this equation are constructed by using the multiplier method.

scholarly journals Time fractional modified KdV-type equations: Lie symmetries, exact solutions and conservation laws

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 480-488
Author(s):  
Fangqin He ◽  
Lianzhong Li
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Symmetries ◽  
Symmetry Reductions ◽  
Kdv Type Equations

Abstract In the paper, we research a time fractional modified KdV-type equations.We give the symmetry reductions and exact solutions of the equations, and we investigate the convergence of the solutions. In addition, the conservation laws of the equations are constructed.

Rosenau-KdV Equation Coupling with the Rosenau-RLW Equation: Conservation Laws and Exact Solutions

2017 ◽  
Vol 18 (6) ◽  
pp. 451-456 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Abdullahi Rashid Adem
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Vries Equation ◽  
Kdv Equation ◽  
Long Wave ◽  
Rlw Equation ◽  
Kudryashov Method ◽  
Regularized Long Wave Equation ◽  
De Vries

AbstractWe compute the conservation laws for the Rosenau-Kortweg de Vries equation coupling with the Regularized Long-Wave equation using Noether’s approach through a remarkable method of increasing the order of the Rosenau-KdV-RLW equation. Furthermore, exact solutions for the Rosenau- KdV-RLW equation are acquired by employing the Kudryashov method.

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