I am using Maple to solve a complex equation. My idea is to separate real and imaginary parts and then solve a set of the equation when both real and imaginary parts are zero. the following are the equation and the way I made real and imaginary parts;
eq:= (K*( Q*sinh(K)*cosh(Q)-K*cosh(K)*sinh(Q))*(1+s*K^2)+p*(-4*K^2*Q*(K^2+Q^2)+Q*(Q^4+2*K^2*Q^2+5*K^4)*cosh(K)*cosh(Q)-K*(Q^4+6*K^2*Q^2+K^4)*sinh(K)*sinh(Q)))/(K^2*Q*cosh(Q)):
so the K and the Q are both complex variables and p and s are constant.
therefore the real and imaginary parts of the equation are
finally, I tried to solve it as following
the problem is that Maple can not solve it and returns the command. I know that there is solutions. How can I solve this equation?
the maple file is attached.mapleprime.mw
I guess Maple use Newton method to solve equation or system of equations. Is there an alternative? I mean what are the possible methods?