Solutions of generalized simple wave type of magnetic fluid

Meleshko, Sergey V.; Moyo, Sibusiso; Webb, G. M.

doi:10.1016/j.cnsns.2021.105991

Cited by 8 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, the method of differential constraints was also used to determine the exact solution of quasilinear systems depending on various applications like p-systems with relaxation conditions (Curró, and Manganaro 19 ), for Chaplygin gas model (Kumar and Radha 20 ), for nonhomogeneous shallow water equations (Sueet et al 21 ), and for the homogeneous p-system (Manganaro et al 22 ). Recently, Meleskho et al 23 discussed the generalized simple wave solution for a magnetic fluid using the differential constraint method and also applied it to systems of equations written in Riemann invariants. 24 Moreover, Chaiyasena et al 25 discussed the generalized Riemann waves and their adjoinment through a shock wave.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Riemann problems for generalized gas dynamics

Kumar

Radha

2023

Stud Appl Math

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…). Recently, Meleskho et al 23 . discussed the generalized simple wave solution for a magnetic fluid using the differential constraint method and also applied it to systems of equations written in Riemann invariants 24 .…”

Section: Introductionmentioning

confidence: 99%

Riemann problems for generalized gas dynamics

Kumar

Radha

2023

Stud Appl Math

View full text Add to dashboard Cite

show abstract

Double wave solutions for a hyperbolic model describing nerve fiber

Manganaro¹,

Rizzo²

2023

Ricerche mat

View full text Add to dashboard Cite

Noether’s theorems and conservation laws in magnetohydrodynamics and Chew–Goldberger–Low plasmas

Webb,

Anco,

Meleshko

et al. 2024

Rev. Mod. Plasma Phys.

View full text Add to dashboard Cite

The ideal magnetohydrodynamic (MHD) equations and the ideal Chew–Goldberger–Low (CGL) plasma equations are studied using Lagrangian field theory methods. Action principles for the equations are developed and used to obtain conservation laws using Noether’s theorems. The Galilean group admitted by the equations leads to (i) energy, (ii) momentum, (iii) center of mass, and (iv) angular momentum conservation laws corresponding to the time translation, space translation, Galilean boosts, and rotational symmetries, respectively. The cross-helicity conservation law is a consequence of a fluid relabeling symmetry, and is local or non-local depending on whether the entropy gradient ($$\nabla S$$ ∇ S ) is perpendicular to the magnetic field induction $$\textbf{B}$$ B or otherwise. The point Lie symmetries of the MHD and CGL equations consist of Galilean transformations and scalings. Noether’s second theorem is used to derive a wave action conservation equation for a linear non-WKBJ Alfvén waves model for stellar winds. Recent symmetry group investigation of the Lagrangian MHD equations in two space dimensions are discussed.

show abstract

Solutions of generalized simple wave type of magnetic fluid

Cited by 8 publications

References 7 publications

Riemann problems for generalized gas dynamics

Riemann problems for generalized gas dynamics

Double wave solutions for a hyperbolic model describing nerve fiber

Noether’s theorems and conservation laws in magnetohydrodynamics and Chew–Goldberger–Low plasmas

Contact Info

Product

Resources

About