Conservation laws and exact solutions of a class of non linear regularized long wave equations via double reduction theory and Lie symmetries

2013 ◽  
Vol 18 (4) ◽  
pp. 826-834 ◽  
Author(s):  
R. Naz ◽  
M.D. Khan ◽  
I. Naeem
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Wave Equations ◽  
Lie Symmetries ◽  
Reduction Theory ◽  
Double Reduction ◽  
Long Wave ◽  
Non Linear

scholarly journals Conservation Laws and Exact Solutions of Generalized Nonlinear System and Nizhink-Novikov-Veselov Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
A. A. Zaidi ◽  
M. D. Khan ◽  
I. Naeem
Keyword(s):  
Nonlinear System ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Symmetries ◽  
Reduction Theory ◽  
Lie Point Symmetries ◽  
Double Reduction

The Lie symmetries, conservation laws, and exact solutions of a generalized nonlinear system and a (2+1)-dimensional generalized Nizhink-Novikov-Veselov (NNV) equation, arising in the study of hydrodynamics, are investigated. The multiplier approach is employed to compute the conservation laws for systems under consideration. The Lie point symmetries are derived and the association between symmetries and conserved vectors are established using symmetries conservation laws relationship. The double reduction theory is utilized which results in the reduction and exact solutions of models under investigation. All cases are discussed in detail and new solutions are determined.

Symmetry Reduction, Exact Solutions, and Conservation Laws of the (2+1)-Dimensional Dispersive Long Wave Equations

2009 ◽  
Vol 64 (9-10) ◽  
pp. 597-603 ◽  
Author(s):  
Zhong Zhou Dong ◽  
Yong Chen
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Symmetry Group ◽  
Infinite Number ◽  
Wave Equations ◽  
Direct Method ◽  
Discrete Groups ◽  
Point Symmetry Group ◽  
Long Wave ◽  
Full Symmetry

By means of the generalized direct method, we investigate the (2+1)-dimensional dispersive long wave equations. A relationship is constructed between the new solutions and the old ones and we obtain the full symmetry group of the (2+1)-dimensional dispersive long wave equations, which includes the Lie point symmetry group S and the discrete groups D. Some new forms of solutions are obtained by selecting the form of the arbitrary functions, based on their relationship. We also find an infinite number of conservation laws of the (2+1)-dimensional dispersive long wave equations.

Exact solutions and conservation laws for coupled generalized Korteweg–de Vries and quintic regularized long wave equations

2005 ◽  
Vol 63 (5-7) ◽  
pp. e1425-e1434 ◽  
Author(s):  
S. Hamdi ◽  
W.H. Enright ◽  
W. E Schiesser ◽  
J.J. Gottlieb
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Wave Equations ◽  
Long Wave ◽  
De Vries

scholarly journals Double Reduction Analysis of Benjamin, DGH and Generalized DGH Equations

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Higher Order ◽  
Reduction Theory ◽  
Double Reduction ◽  
Linear Evolution ◽  
Holm Equation ◽  
Linear Evolution Equation ◽  
Non Linear ◽  
Benjamin Equation

The exact solutions of non-linear evolution equation, Benjamin equation, Dullin-Gottwald-Holm (DGH) equation and generalized Dullin-Gottwald-Holm equation are established using the conserved vectors. The multiplier approach is applied to construct the conserved vectors for equations under consideration. For non-linear evolution equation three conserved vectors and for Benjamin equation four conserved vectors are obtained. The conserved vectors for DGH and generalized DGH equations were reported in [1]. The higher order multiplier is considered for DGH equation and a new conserved vector is found. The double reduction theory is utilized to obtain various exact solutions for Benjamin equation, DGH equation and generalized DGH equation.

scholarly journals Reductions and New Exact Solutions of ZK, Gardner KP, and Modified KP Equations via Generalized Double Reduction Theorem

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naz ◽  
Z. Ali ◽  
I. Naeem
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
First Integral ◽  
Second Order ◽  
Lie Symmetries ◽  
Reduction Theorem ◽  
Explicit Solutions ◽  
Double Reduction ◽  
Zk Equation ◽  
New Exact Solutions

We study here the Lie symmetries, conservation laws, reductions, and new exact solutions of (2+1) dimensional Zakharov-Kuznetsov (ZK), Gardner Kadomtsev-Petviashvili (GKP), and Modified Kadomtsev-Petviashvili (MKP) equations. The multiplier approach yields three conservation laws for ZK equation. We find the Lie symmetries associated with the conserved vectors, and three different cases arise. The generalized double reduction theorem is then applied to reduce the third-order ZK equation to a second-order ordinary differential equation (ODE) and implicit solutions are established. We use the Sine-Cosine method for the reduced second-order ODE to obtain new explicit solutions of ZK equation. The Lie symmetries, conservation laws, reductions, and exact solutions via generalized double reduction theorem are computed for the GKP and MKP equations. Moreover, for the GKP equation, some new explicit solutions are constructed by applying the first integral method to the reduced equations.

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
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