Self-adjointness and conservation laws for Kadomtsev–Petviashvili–Burgers equation

2015 ◽  
Vol 23 ◽  
pp. 123-128 ◽  
Author(s):  
Long Wei ◽  
Jiezi Zhang
Keyword(s):  
Conservation Laws ◽  
Burgers Equation

scholarly journals Self-Adjointness and Conservation Laws of Frobenius Type Equations

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1987
Author(s):  
Haifeng Wang ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Burgers Equation ◽  
Kdv Equation ◽  
The Self ◽  
Kp Equation ◽  
Commutative Subalgebra ◽  
Kompaneets Equation ◽  
Dym Equation ◽  
Harry Dym Equation

The Frobenius KDV equation and the Frobenius KP equation are introduced, and the Frobenius Kompaneets equation, Frobenius Burgers equation and Frobenius Harry Dym equation are constructed by taking values in a commutative subalgebra Z2ε in the paper. The five equations are selected as examples to help us study the self-adjointness of Frobenius type equations, and we show that the first two equations are quasi self-adjoint and the last three equations are nonlinear self-adjointness. It follows that we give the symmetries of the Frobenius KDV and the Frobenius KP equation in order to construct the corresponding conservation laws.

scholarly journals Exact solutions and conservation laws for the modified equal width-Burgers equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 795-800 ◽  
Author(s):  
Chaudry Masood Khalique ◽  
Innocent Simbanefayi
Keyword(s):  
Conservation Laws ◽  
Burgers Equation ◽  
Expansion Method ◽  
Momentum Conservation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Lie Symmetry Method ◽  
Long Wave ◽  
Symmetry Method ◽  
Conservation Theorem

AbstractIn this paper we study the modified equal width-Burgers equation, which describes long wave propagation in nonlinear media with dispersion and dissipation. Using the Lie symmetry method in conjunction with the (G'/G)− expansion method we construct its travelling wave solutions. Also, we determine the conservation laws by invoking the new conservation theorem due to Ibragimov. As a result we obtain energy and linear momentum conservation laws.

Shock Waves, Variational Principle and Conservation Laws of a Schamel–Zakharov–Kuznetsov–Burgers Equation in a Magnetised Dust Plasma

2018 ◽  
Vol 73 (8) ◽  
pp. 693-704 ◽  
Author(s):  
O.H. EL-Kalaawy ◽  
Engy A. Ahmed
Keyword(s):  
Variational Principle ◽  
Conservation Laws ◽  
Acoustic Waves ◽  
Burgers Equation ◽  
Special Functions ◽  
Nonlinear Propagation ◽  
Ion Acoustic Waves ◽  
New Exact Solutions ◽  
Kudryashov Method ◽  
Plasma Dust

AbstractIn this article, we investigate a (3+1)-dimensional Schamel–Zakharov–Kuznetsov–Burgers (SZKB) equation, which describes the nonlinear plasma-dust ion acoustic waves (DIAWs) in a magnetised dusty plasma. With the aid of the Kudryashov method and symbolic computation, a set of new exact solutions for the SZKB equation are derived. By introducing two special functions, a variational principle of the SZKB equation is obtained. Conservation laws of the SZKB equation are obtained by two different approaches: Lie point symmetry and the multiplier method. Thus, the conservation laws here can be useful in enhancing the understanding of nonlinear propagation of small amplitude electrostatic structures in the dense, dissipative DIAWs’ magnetoplasmas. The properties of the shock wave solutions structures are analysed numerically with the system parameters. In addition, the electric field of this solution is investigated. Finally, we will study the physical meanings of solutions.

Explicit Solutions and Conservation Laws of a Coupled Burgers’ Equation

2017 ◽  
Vol 72 (9) ◽  
pp. 789-793
Author(s):  
Bo Xue ◽  
Fang Li ◽  
Yihao Li ◽  
Mingming Sun
Keyword(s):  
Conservation Laws ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Burgers Equation ◽  
Integrable Equation ◽  
Explicit Solutions ◽  
Spectral Problems ◽  
Coupled Burgers Equation

AbstractBased on the gauge transformation between the corresponding 3×3 matrix spectral problems, N-fold Darboux transformation for a coupled Burgers’ equation is constructed. Considering the N=1 case of the derived Darboux transformation, explicit solutions for the coupled Burgers’ equation are given and their figures are plotted. Moreover, conservation laws of this integrable equation are deduced.

The Sharma–Tasso–Olver–Burgers equation: Its conservation laws and kink solitons

2021 ◽  
Author(s):  
Kamyar Hosseini ◽  
Arzu Akbulut ◽  
Dumitru Baleanu ◽  
Soheil Salahshour
Keyword(s):  
Conservation Laws ◽  
Burgers Equation ◽  
Lie Symmetries ◽  
Adjoint Equations ◽  
Current Investigation ◽  
Dynamical Features ◽  
Exponential Methods ◽  
First Time

Abstract The present paper deals with the Sharma–Tasso–Olver–Burgers equation (STOBE) and its conservation laws and kink solitons. More precisely, the formal Lagrangian, Lie symmetries, and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws. Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods. Diverse graphs in 3D postures are formally portrayed to reveal the dynamical features of kink solitons. According to the authors’ knowledge, the outcomes of the current investigation are new and have been listed for the first time.

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