scholarly journals Optimal System and New Approximate Solutions of a Generalized Ames’s Equation

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1230
Author(s):  
Marianna Ruggieri ◽  
Maria Paola Speciale
Keyword(s):  
Lie Algebra ◽  
Algebraic Structure ◽  
Approximate Solutions ◽  
Optimal System ◽  
Approximate Symmetry ◽  
Invariant Solutions ◽  
One Dimensional

In this paper, by applying Valenti’s theory for the approximate symmetry, we introduce and define the concept of a one-dimensional optimal system of approximate subalgebras for a generalized Ames’s equation; furthermore, the algebraic structure of the approximate Lie algebra is discussed. New approximately invariant solutions to the equation are found.

scholarly journals Optimal System and Group Invariant Solutions of the Whitham-Broer-Kaup System

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Xiaorui Hu ◽  
Yongyang Jin ◽  
Kai Zhou
Keyword(s):  
Lie Algebra ◽  
Nonlinear Waves ◽  
Optimal System ◽  
Invariant Solutions ◽  
One Dimensional ◽  
Nonlocal Symmetries ◽  
Group Invariant ◽  
Group Invariant Solutions

From the nonlocal symmetries of the Whitham-Broer-Kaup system, an eight-dimensional Lie algebra is found and the corresponding one-dimensional optimal system is constructed to provide an inequivalent classification. Six types of inequivalent group invariant solutions are demonstrated, some of which reflect the interactions between soliton and other nonlinear waves.

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.

scholarly journals SYMMETRY ANALYSIS OF TELEGRAPH EQUATION

2011 ◽  
Vol 04 (01) ◽  
pp. 117-126
Author(s):  
Mehdi Nadjafikhah ◽  
Seyed-Reza Hejazi
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Telegraph Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Group Method ◽  
Parameter Group ◽  
One Dimensional

Lie symmetry group method is applied to study the telegraph equation. The symmetry group and one-parameter group associated to the symmetries with the structure of the Lie algebra symmetries are determined. The reduced version of equation and its one-dimensional optimal system are given.

scholarly journals Approximate Symmetries of the Harry Dym Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Mehdi Nadjafikhah ◽  
Parastoo Kabi-Nejad
Keyword(s):  
Lie Algebra ◽  
Optimal System ◽  
Differential Invariants ◽  
Approximate Symmetries ◽  
One Dimensional ◽  
First Order ◽  
Optimal System Of Subalgebras ◽  
Dym Equation ◽  
The One ◽  
Harry Dym Equation

We derive the first-order approximate symmetries for the Harry Dym equation by the method of approximate transformation groups proposed by Baikov et al. (1989, 1996). Moreover, we investigate the structure of the Lie algebra of symmetries of the perturbed Harry Dym equation. We compute the one-dimensional optimal system of subalgebras as well as point out some approximately differential invariants with respect to the generators of Lie algebra and optimal system.

scholarly journals Optimal System and Invariant Solutions of a New AKNS Equation with Time-Dependent Coefficients

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 522
Author(s):  
Na Liu
Keyword(s):  
Traveling Wave Solutions ◽  
Optimal System ◽  
Time Dependent ◽  
Lie Point Symmetries ◽  
Invariant Solutions ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction ◽  
One Dimensional ◽  
Power Series Solutions ◽  
Akns Equation

The Lie point symmetries are reported by performing the Lie symmetry analysis to the Ablowitz-Kaup-Newell-Suger (AKNS) equation with time-dependent coefficients. In addition, the optimal system of one-dimensional subalgebras is constructed. Based on this optimal system, several categories of similarity reduction and some new invariant solutions for the equation are obtained, which include power series solutions and travelling and non-traveling wave solutions.

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 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.

Lie Symmetries, One-Dimensional Optimal System and Group Invariant Solutions for the Ripa System

2019 ◽  
Vol 20 (6) ◽  
pp. 713-723 ◽  
Author(s):  
Pabitra Kumar Pradhan ◽  
Manoj Pandey
Keyword(s):  
Adjoint Representation ◽  
Group Classification ◽  
Optimal System ◽  
Invariant Solutions ◽  
Horizontal Temperature Gradient ◽  
One Dimensional ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
The One ◽  
Complete Symmetry Group

AbstractA complete symmetry group classification for the system of shallow water equations with the horizontal temperature gradient, also known as Ripa system, is presented. A rigorous and systematic procedure based on the general invariants of the adjoint representation is used to construct the one-dimensional optimal system of the Lie algebra. The complete inequivalence class of the group invariant solutions are obtained by using the one-dimensional optimal system. One such solution of the Ripa system is used to study the evolutionary behaviour of the discontinuity wave.

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