i am looking for special solution i want give the maple equation and give what answer i want with condition for example i just want thus solution which is A_0,A_1,B_1 not equal to zero and other parameter like (w,lambda,k) are free just this three not equal to zero.

restart
with(SolveTools);
with(LinearAlgebra);
eq12 := -alpha*k^2*A[0] - alpha*k^2*A[1] - alpha*k^2*B[1] + A[0]^3*beta[4] + (3*A[0]^2)*A[1]*beta[4] + (3*A[0]^2)*B[1]*beta[4] + (3*A[0])*A[1]^2*beta[4] + (6*A[0])*A[1]*B[1]*beta[4] + (3*A[0])*B[1]^2*beta[4] + A[1]^3*beta[4] + (3*A[1]^2)*B[1]*beta[4] + (3*A[1])*B[1]^2*beta[4] + B[1]^3*beta[4] + A[0]^2*beta[3] + (2*A[0])*A[1]*beta[3] + (2*A[0])*B[1]*beta[3] + A[1]^2*beta[3] + (2*A[1])*B[1]*beta[3] + B[1]^2*beta[3] - w*A[0] - w*A[1] - w*B[1] = 0
eq10 := (2*alpha)*k^2*A[1] - (2*alpha)*k^2*B[1] - (8*alpha)*lambda^2*A[1] + (8*alpha)*lambda^2*B[1] - (8*gamma)*lambda^2*A[1] + (8*gamma)*lambda^2*B[1] - (6*A[0]^2)*A[1]*beta[4] + (6*A[0]^2)*B[1]*beta[4] - (12*A[0])*A[1]^2*beta[4] + (12*A[0])*B[1]^2*beta[4] - (6*A[1]^3)*beta[4] - (6*A[1]^2)*B[1]*beta[4] + (6*A[1])*B[1]^2*beta[4] + (6*B[1]^3)*beta[4] - (4*A[0])*A[1]*beta[3] + (4*A[0])*B[1]*beta[3] - (4*A[1]^2)*beta[3] + (4*B[1]^2)*beta[3] + (2*w)*A[1] - (2*w)*B[1] = 0
eq8 := -(3*A[1]^2)*B[1]*beta[4] - (3*A[1])*B[1]^2*beta[4] - (2*A[0])*A[1]*beta[3] - (2*A[0])*B[1]*beta[3] + w*A[1] + w*B[1] - (3*A[0]^2)*B[1]*beta[4] + alpha*k^2*A[1] + alpha*k^2*B[1] - (3*A[0]^2)*A[1]*beta[4] + (3*alpha)*k^2*A[0] + (32*alpha)*lambda^2*A[1] + (32*alpha)*lambda^2*B[1] + (32*gamma)*lambda^2*A[1] + (32*gamma)*lambda^2*B[1] - (3*A[0]^3)*beta[4] + (15*A[0])*A[1]^2*beta[4] - (18*A[0])*A[1]*B[1]*beta[4] + (15*A[0])*B[1]^2*beta[4] + (15*A[1]^3)*beta[4] + (15*B[1]^3)*beta[4] - (3*A[0]^2)*beta[3] + (5*A[1]^2)*beta[3] - (6*A[1])*B[1]*beta[3] + (5*B[1]^2)*beta[3] + (3*w)*A[0] = 0
eq6 := -(4*alpha)*k^2*A[1] + (4*alpha)*k^2*B[1] - (48*alpha)*lambda^2*A[1] + (48*alpha)*lambda^2*B[1] - (48*gamma)*lambda^2*A[1] + (48*gamma)*lambda^2*B[1] + (12*A[0]^2)*A[1]*beta[4] - (12*A[0]^2)*B[1]*beta[4] - (20*A[1]^3)*beta[4] + (12*A[1]^2)*B[1]*beta[4] - (12*A[1])*B[1]^2*beta[4] + (20*B[1]^3)*beta[4] + (8*A[0])*A[1]*beta[3] - (8*A[0])*B[1]*beta[3] - (4*w)*A[1] + (4*w)*B[1] = 0
eq4 := -(3*A[1]^2)*B[1]*beta[4] - (3*A[1])*B[1]^2*beta[4] - (2*A[0])*A[1]*beta[3] - (2*A[0])*B[1]*beta[3] + w*A[1] + w*B[1] - (3*A[0]^2)*B[1]*beta[4] + alpha*k^2*A[1] + alpha*k^2*B[1] - (3*A[0]^2)*A[1]*beta[4] - (3*alpha)*k^2*A[0] + (32*alpha)*lambda^2*A[1] + (32*alpha)*lambda^2*B[1] + (32*gamma)*lambda^2*A[1] + (32*gamma)*lambda^2*B[1] + (3*A[0]^3)*beta[4] - (15*A[0])*A[1]^2*beta[4] + (18*A[0])*A[1]*B[1]*beta[4] - (15*A[0])*B[1]^2*beta[4] + (15*A[1]^3)*beta[4] + (15*B[1]^3)*beta[4] + (3*A[0]^2)*beta[3] - (5*A[1]^2)*beta[3] + (6*A[1])*B[1]*beta[3] - (5*B[1]^2)*beta[3] - (3*w)*A[0] = 0
eq2 := (2*alpha)*k^2*A[1] - (2*alpha)*k^2*B[1] - (8*alpha)*lambda^2*A[1] + (8*alpha)*lambda^2*B[1] - (8*gamma)*lambda^2*A[1] + (8*gamma)*lambda^2*B[1] - (6*A[0]^2)*A[1]*beta[4] + (6*A[0]^2)*B[1]*beta[4] + (12*A[0])*A[1]^2*beta[4] - (12*A[0])*B[1]^2*beta[4] - (6*A[1]^3)*beta[4] - (6*A[1]^2)*B[1]*beta[4] + (6*A[1])*B[1]^2*beta[4] + (6*B[1]^3)*beta[4] - (4*A[0])*A[1]*beta[3] + (4*A[0])*B[1]*beta[3] + (4*A[1]^2)*beta[3] - (4*B[1]^2)*beta[3] + (2*w)*A[1] - (2*w)*B[1] = 0
eq0 := alpha*k^2*A[0] - alpha*k^2*A[1] - alpha*k^2*B[1] - A[0]^3*beta[4] + (3*A[0]^2)*A[1]*beta[4] + (3*A[0]^2)*B[1]*beta[4] - (3*A[0])*A[1]^2*beta[4] - (6*A[0])*A[1]*B[1]*beta[4] - (3*A[0])*B[1]^2*beta[4] + A[1]^3*beta[4] + (3*A[1]^2)*B[1]*beta[4] + (3*A[1])*B[1]^2*beta[4] + B[1]^3*beta[4] - A[0]^2*beta[3] + (2*A[0])*A[1]*beta[3] + (2*A[0])*B[1]*beta[3] - A[1]^2*beta[3] - (2*A[1])*B[1]*beta[3] - B[1]^2*beta[3] + w*A[0] - w*A[1] - w*B[1] = 0
COEFFS := solve({eq0, eq10, eq12, eq2, eq4, eq6, eq8}, {k, lambda, w, A[0], A[1], B[1]})