In this series of papers we examine magnetic reconnection in a domain where the magnetic field does not vanish and the non-ideal region is localised in space. In a previous paper we presented a technique for obtaining analytical solutions to the stationary resistive MHD equations in such a situation and examined specific examples of non-ideal reconnective solutions. Here we further develop the ...

This paper uses the weighted L$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. When all variables are integer it finds the whole set of efficient solutions. In each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...

We propose a technique for obtaining solutions to ordinary differential equations. A system of differential equations sometimes has multiple solutions with distinct features. Prime ideal decomposition can be used for extracting the desired solution from these solutions. Solutions to algebraic equations contain many parameters, and in such a case, prime ideal decomposition is less tractable. As ...

In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the classification by conjugacy classes of r-dimensional subalgebras (1 ≤ r ≤ 4) was already known. So we restrict our study to the three-dimensional Galilean-similitude su...

In this paper, we address the problem of weak solutions of Yudovich type for the inviscid MHD equations in two dimensions. The local-in-time existence and uniqueness of these solutions sound to be hard to achieve due to some terms involving Riesz transforms in the vorticity-current formulation. We shall prove that the vortex patches with smooth boundary offer a suitable class of initial data fo...