Solition problems with Matlab (12 PDE with 8 variables))

[tiantsai]

Hi, I am a master student comes from USM in Malaysia. I don't know my problem should placed on differential forum or high energy physics forum. Anywhere, My current study is high energy physics subject and my main study is focus on monopole instanton solution in static form which did not include time, i using the Lagrangian to generate out the 12 set equations of motion with 8 variables, the software that i use is Matlab with Optimization toolbox- the algorithm that i use inside the package is trusted reflective region and the numerical method that i used is finite difference method. However, it did not converge. I have tried to reproduce the Jutta Kunz paper-monopoles solution with 6 set of partial differential equation with 6 variables and its work well and i also obtain the Higgs field $\Phi(r,\theta)$ of monopole successfully. The variables that in the set of equations of motion is in r and $\theta$ form which means as A(r,$\theta$). So any suggestion for using Matlab to solve the 12 set equations of motion (PDE form) with 8 variables.

 

[Dickfore]

I am very intriqued how you managed to "generate" more equations than unknown functions.

 

[tiantsai]

My professor say its is a overdetermined system with because the number of partial equations is more than the variables and suppose it can give us a fine numerical solution for each variables but my program still cannot converge...

 

[tiantsai]

Well i am using the ansatz which include gauge and Higgs variable that in the form of spherical coordinate (also include internal and external space), so putting inside the Lagrangian and its generate out 12 equations of motion with 8 variables.

 

[Dickfore]

what do you mean by "variables"?