Lie symmetries, conservation laws and exact solutions for time fractional Ito equation

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.

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

Journal of Applied Mathematics ◽

10.1155/2014/849361 ◽

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.”

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Symmetries and conservation laws of a damped Boussinesq equation

International Journal of Modern Physics B ◽

10.1142/s0217979216400129 ◽

2016 ◽

Vol 30 (28n29) ◽

pp. 1640012 ◽

Cited By ~ 1

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.

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

Open Physics ◽

10.1515/phys-2019-0049 ◽

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.

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New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4035408 ◽

2017 ◽

Vol 12 (4) ◽

Cited By ~ 5

Author(s):

Gülden Gün Polat ◽

Teoman Özer

Keyword(s):

Conservation Laws ◽

Exact Solutions ◽

First Integrals ◽

Lie Symmetries ◽

Jacobi Method ◽

Emden Equation ◽

Mathematical Connections ◽

Integrating Factors

This study deals with the determination of Lagrangians, first integrals, and integrating factors of the modified Emden equation by using Jacobi and Prelle–Singer methods based on the Lie symmetries and λ-symmetries. It is shown that the Jacobi method enables us to obtain Jacobi last multipliers by means of the Lie symmetries of the equation. Additionally, via the Lie symmetries of modified Emden equation, we analyze some mathematical connections between λ-symmetries and Prelle–Singer method. New and nontrivial Lagrangian forms, conservation laws, and exact solutions of the equation are presented and discussed.

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

Mathematical Problems in Engineering ◽

10.1155/2018/3565393 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14 ◽

Cited By ~ 1

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.

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