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Simultaneous solving of two equations for extraction of one variable

Omer Tzuk
Posted 9 years ago

I have the following system of equations $$ exp1 = c \partial{\chi} uB + 2 uB (uB h1 + vB h2) + \nu vB + \beta vB (uB^2 + vB^2) + \alpha \partial{\chi}^2 v_B == 0\ exp2 = c \partial{\chi} vB + 2 vB (uB h1 + vB h2) - \nu uB - \beta uB (uB^2 + vB^2) - \alpha \partial{\chi}^2 u_B == 0 $$ where I have $$h1=\text{TrigToExp}[\tanh (k x)];\h2=\text{TrigToExp}[\text{sech}(k x)];\ uB=\sqrt{\gamma +\mu } \text{TrigToExp}[\tanh (k x)]\ vB=\sqrt{\mu -3 \gamma } \text{TrigToExp}[\text{sech}(k x)]

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POSTED BY: Omer Tzuk
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Did you try SolveAlways?
POSTED BY: Gianluca Gorni

Your equation is linear in c but it is trascendental in k. You get a closed-form result for example if you solve first for c in one of the equation, replace into the other, and give specific values for the parameters:

Solve[exp2 /. 
   Solve[exp1, c] /. {\[Mu] -> 4, \[Gamma] -> 0, \[Alpha] -> 
    1, \[Beta] -> 1, \[Nu] -> 1}, x]

It is not clear to me what you mean with the third argument in Solve[{exp1,exp2},{c},{k}]
POSTED BY: Gianluca Gorni
Omer Tzuk
Omer Tzuk
Posted 9 years ago

But what if I want to solve for c for any values of the parameters? This system does not allow me to do it?
POSTED BY: Omer Tzuk
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