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BvU said:Hello eahaidar,
Don't you think that is a bit terse ? Some explanation of the variables might be in order. Complex variables ? Probably: in particular: g -- if g is real nothing happens.
Below is the homework template; you case may not be a homework exercise, but the systematic approach might be useful anyway !
1. The problem statement, all variables and given/known data
2. Homework Equations
3. The Attempt at a Solution
I still see an ##|A_0|^2## sitting there. is it constant and equal to 1 ? But even d(I0) /dz = (d( ISBS)/dz)/A02 + d(I STOKES)/dz is enough to reduce this to a two differential equations problem -- doesn't change the suggestion.eahaidar said:What I meant from 1=2 +3 is that notice that d(I0) /dz = d( ISBS)/dz + d(I STOKES)/dz.
So is this a set of differential equations in z only, or is there some time dependence that plays a role too ?eahaidar said:SBS and STOKES represent 2 light waves counter propagating the forward wave of index 0 which puts me in trouble since initally at z=0 I only have the forward wave
I usually use MATLAB for any simulation. I went through the equations. With the help of a colleague, we managed to reduce the coupled equations to a single equation. I will update you on that once i get to the bottom of this equation which includes the 3 variables. Again thanks for your help and would love to learn your integrator. Sounds fun to use.BvU said:(Sorry, I missed this alert during the weekend).
Program is a dynamic simulation program for the chemical industry, called aspen custom modeler. But all I use is the integrator, so I didn't mention it. It has lousy graphics, so picture is made by moving the data to excel. Also easier to do further analysis: take logarithm, fit that to a polynomial, to see if it's a simple exponential. It is not:
(##\ \ln(I_{\rm stokes} ) = -2.6356 - 0.0939 z + 0.0011 z^2\ ## )
Got the curves by doing the forward integration from z = 0 to 10. Chose C2 = I0(0) = 0.1 and played around with ISBS(0) and Istokes(0) until they ended up at the same value. I called that C1. Normally you would let the computer do the guessing (shooting method) with a reasonable efficiency.
So still no joy finding something analytical.
What tools do you have at your disposal for this ?
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Coupled nonlinear differential equations are a type of mathematical model used to describe the relationship between two or more variables that are changing over time. They involve nonlinear functions, meaning that the rate of change of a variable is not directly proportional to the value of that variable.
Coupled nonlinear differential equations have many applications in physics, engineering, and biology. They are used to model complex systems such as chemical reactions, population dynamics, and electrical circuits.
There are various methods for solving coupled nonlinear differential equations, including numerical methods, analytical methods, and computer simulations. These methods involve manipulating the equations to find a solution that satisfies all of the given conditions.
Yes, depending on the specific equations and initial conditions, coupled nonlinear differential equations can have multiple solutions or even no solution. In some cases, the equations may have unstable solutions that are not physically meaningful.
Solving coupled nonlinear differential equations can be challenging due to the complexity of the equations and the potential for multiple solutions. It often requires advanced mathematical techniques and computational resources. In addition, the accuracy and precision of the solutions can be affected by the initial conditions and the numerical methods used.