scholarly journals Exact solutions of equal-width equation and its conservation laws

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 505-511 ◽  
Author(s):  
Chaudry Masood Khalique ◽  
Karabo Plaatjie ◽  
Innocent Simbanefayi
Keyword(s):  
Wave Propagation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Optimal System ◽  
Invariant Solutions ◽  
Cnoidal Waves ◽  
Dispersion Process ◽  
One Dimensional ◽  
Linear Medium ◽  
D Wave

Abstract In this work we investigate the equal-width equation, which is used for simulation of (1-D) wave propagation in non-linear medium with dispersion process. Firstly, Lie symmetries are determined and then used to establish an optimal system of one-dimensional subalgebras. Thereafter with its aid we perform symmetry reductions and compute new invariant solutions, which are snoidal and cnoidal waves. Additionally, the conservation laws for the aforementioned equation are established by invoking multiplier method and Noether’s theorem.

scholarly journals On optimal system, exact solutions and conservation laws of the modified equal-width equation

2018 ◽  
Vol 3 (2) ◽  
pp. 409-418 ◽  
Author(s):  
Chaudry Masood Khalique ◽  
Oke Davies Adeyemo ◽  
Innocent Simbanefayi
Keyword(s):  
Wave Propagation ◽  
Conservation Laws ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Invariant Solutions ◽  
Nonlinear Media ◽  
One Dimensional ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Dimensional Wave

AbstractIn this paper we study the modified equal-width equation, which is used in handling simulation of a single dimensional wave propagation in nonlinear media with dispersion processes. Lie point symmetries of this equation are computed and used to construct an optimal system of one-dimensional subalgebras. Thereafter using an optimal system of one-dimensional subalgebras, symmetry reductions and new group-invariant solutions are presented. The solutions obtained are cnoidal and snoidal waves. Furthermore, conservation laws for the modified equal-width equation are derived by employing two different methods, the multiplier method and Noether approach.

scholarly journals Exact Solutions and Conservation Laws of the (3 + 1)-Dimensional B-Type Kadomstev–Petviashvili (BKP)-Boussinesq Equation

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 97 ◽  
Author(s):  
Ben Gao ◽  
Yao Zhang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Boussinesq Equation ◽  
Lie Symmetry ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Reduced Equations ◽  
Tanh Method ◽  
Similarity Reductions

In this paper, Lie symmetry analysis is presented for the (3 + 1)-dimensional BKP-Boussinesq equation, which seriously affects the dispersion relation and the phase shift. To start with, we derive the Lie point symmetry and construct the optimal system of one-dimensional subalgebras. Moreover, according to the optimal system, similarity reductions are investigated and we obtain exact solutions of reduced equations by means of the Tanh method. In the end, we establish conservation laws using Ibragimov’s approach.

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.

scholarly journals Approximate Symmetry Analysis and Approximate Conservation Laws of Perturbed KdV Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yu-Shan Bai ◽  
Qi Zhang
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Symmetry Algebra ◽  
Optimal System ◽  
Approximate Symmetry ◽  
Invariant Solutions ◽  
Approximate Symmetries ◽  
One Dimensional ◽  
Perturbed Kdv Equation ◽  
Partial Lagrangian

Approximate symmetries, which are admitted by the perturbed KdV equation, are obtained. The optimal system of one-dimensional subalgebra of symmetry algebra is obtained. The approximate invariants of the presented approximate symmetries and some new approximately invariant solutions to the equation are constructed. Moreover, the conservation laws have been constructed by using partial Lagrangian method.

Group classification and conservation laws of the generalized Klein–Gordon–Fock equation

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640023
Author(s):  
B. Muatjetjeja
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Algebra ◽  
Group Classification ◽  
Noether Symmetries ◽  
Invariant Solutions ◽  
One Dimensional ◽  
Klein Gordon

In the present paper, we perform Lie and Noether symmetries of the generalized Klein–Gordon–Fock equation. It is shown that the principal Lie algebra, which is one-dimensional, has several possible extensions. It is further shown that several cases arise for which Noether symmetries exist. Exact solutions for some cases are also obtained from the invariant solutions of the investigated equation.

scholarly journals Invariant analysis, exact solutions and conservation laws of (2+1)-dimensional time fractional Navier–Stokes equations

2021 ◽  
Vol 477 (2250) ◽  
pp. 20210220
Author(s):  
Xiaoyu Cheng ◽  
Lizhen Wang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Stokes Equations ◽  
Power Series Expansion ◽  
Expansion Method ◽  
Optimal System ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Fractional Differential Operator

In this paper, we investigate the exact solutions and conservation laws of (2 + 1)-dimensional time fractional Navier–Stokes equations (TFNSE). Specifically, Lie symmetries and corresponding one-dimensional optimal system for TFNSE in Riemann–Liouville sense are obtained. Then, based on the admitted symmetries and optimal system, we reduce these equations to one-dimensional equations or (1 + 1)-dimensional fractional partial differential equations (PDEs) with the help of Erdélyi–Kober fractional differential operator and compound variable transformation. In addition, we solve the reduced PDEs applying power series expansion method and invariant subspace method, respectively. Furthermore, the conservation laws of TFNSE are derived using new Noether theorem.

Generalized symmetries and higher-order Conservation laws of the Camassa–Holm equation

2019 ◽  
Vol 9 (2) ◽  
pp. 20-25
Author(s):  
Parastoo Kabi-Nejad ◽  
Keyword(s):  
Vector Field ◽  
Conservation Laws ◽  
Adjoint Representation ◽  
Higher Order ◽  
Optimal System ◽  
Homotopy Formula ◽  
One Dimensional ◽  
Holm Equation ◽  
Generalized Symmetries ◽  
Symmetry Criterion

In the present paper, we derive generalized symmetries of order three of the Camassa–Holm equation by infinite prolongation of a generalized vector field and applying infinitesimal symmetry criterion. In addition, one-dimensional optimal system of Lie subalgebras investigated by applying the adjoint representation. Furthermore, determining equation for multipliers and the 2- dimensional homotopy formula employed to construct higher–order conservation laws for the Camassa–Holm equation.

scholarly journals Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Sixth-Order Nonlinear Ramani Equation

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 341 ◽  
Author(s):  
Aliyu Aliyu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Conservation Laws ◽  
Travelling Wave ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Sixth Order ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Analysis Technique ◽  
Conservation Theorem

In this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli sub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction. We show that the equation is nonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries by invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical interpretations of the acquired results.

Sign in / Sign up

Export Citation Format

Share Document