Generalized Conditional Symmetries, Related Solutions and Conservation Laws of the Grad-Shafranov Equation with Arbitrary Flow

DOI

10.1080/14029251.2017.1375689How to use a DOI?

Keywords

Grad-Schafranov equation; arbitrary magnetic flux; generalized conditional symmetries; symbolic computation; invariant solutions; conservation laws

Abstract

The generalized conditional symmetry (GCS) method is applied to the case of a generalized Grad-Shafranov equation (GGSE) with incompressible flow of arbitrary direction. We investigate the conditions which yield the GGSE that admits a special class of second-order GCSs. Three GCS generators and the associated families of invariant solutions are pointed out. Several plots of the level sets or flux surfaces of the new solutions are displayed. These results extend the recent solutions with 5 parameters recently obtained on the basis of Lie-point symmetries. They could be useful in the study of plasma equilibrium, of transport phenomena, and of magnetohydrodynamic stability. Futher, by making use of the multiplier’s method, three nontrivial conservation laws that are admitted by the concerned equation and which involve arbitrary functions, are highlighted.

Copyright

© 2017 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC license.

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TY  - JOUR
AU  - Rodica Cimpoiasu
PY  - 2021
DA  - 2021/01/06
TI  - Generalized Conditional Symmetries, Related Solutions and Conservation Laws of the Grad-Shafranov Equation with Arbitrary Flow
JO  - Journal of Nonlinear Mathematical Physics
SP  - 531
EP  - 544
VL  - 24
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1375689
DO  - 10.1080/14029251.2017.1375689
ID  - Cimpoiasu2021
ER  -