Generalized Conditional Symmetries, Related Solutions and Conservation Laws of the Grad-Shafranov Equation with Arbitrary Flow
- 10.1080/14029251.2017.1375689How to use a DOI?
- Grad-Schafranov equation; arbitrary magnetic ﬂux; generalized conditional symmetries; symbolic computation; invariant solutions; conservation laws
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.
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
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Cite this article
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 -