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General methods of solving equations deal with solving N equations in N variables and the solutions are usually a set of discrete values. However, for problems with a softly broken symmetry these methods often first find a point which would be a solution if the symmetry were exact, and is thus an approximate solution. After this, the solver needs to move in the direction of the symmetry to find the actual solution, but that can be very difficult if this direction is not a straight line in the space of variables. The solution can often be found much more quickly by adding the generators of the softly broken symmetry as auxiliary variables. This makes the number of variables more than the equations and hence there will be a family of solutions, any one of which would be acceptable. In this paper we present a procedure for finding solutions in this case, and apply it to several simple examples and an important problem in the physics of false vacuum decay. We also provide a Mathematica package that implements Powells hybrid method with the generalization to allow more variables than equations.
Cosmography becomes non-predictive when cosmic data span beyond the red shift limit $zsimeq1 $. This leads to a emph{strong convergence issue} that jeopardizes its viability. In this work, we critically compare the two main solutions of the convergen
We develop methods to study the scalar sector of multi-Higgs models with large discrete symmetry groups that are softly broken. While in the exact symmetry limit, the model has very few parameters and can be studied analytically, proliferation of qua
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of penalty type for the second-order wave
We study the duality cascade of softly broken supersymmetric theories. We investigate the renormalization group (RG) flow of SUSY breaking terms as well as supersymmetric couplings. It is found that the magnitudes of SUSY breaking terms are suppresse
In this note we study the eigenvalue problem for a quadratic form associated with Strichartz estimates for the Schr{o}dinger equation, proving in particular a sharp Strichartz inequality for the case of odd initial data. We also describe an alternati