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Question: How to rewrite nonlinear equations in terms of others to solve a system of them?

Question:How to rewrite nonlinear equations in terms of others to solve a system of them?

MaPal93 175 Maple 2023
solve parameters nonlinear
January 07 2025
0

I have a system of 4 nonlinear equations in 4 lambda variables. I cannot obtain a solution using solve():

4_nonlinear_equations.mw

I can sometimes simplify similar systems by rescaling equations to reduce parameters. With only 3 parameters (sigma_v, sigma_d, sigma_d3) in this case, complexity arises from the interactions of the 4 lambdas in the 4 equations. Upon examining the equations (highlighted in yellow), I suspect hidden symmetries. Is it possible to solve the system by rewriting the equations in terms of each other to find an equivalent system? I am exploring if a smarter and simpler reformulation could lead to a solution. Thank you.
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