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These are questions asked by WA573


with(DEtools); with(LinearAlgebra)

diff(u(x, t), t) = [Matrix([[0, (1/2)*mu*k^2], [2*A^2-(1/2)*mu*k^2, 0]])]*u(x, t)

diff(u(x, t), t) = [Matrix(%id = 36893489823894642308)]*u(x, t)


"where u(x,t)=[u1 u2]^(T) is a vector. The solution of differential equation (1) is u=v*exp(w*t)."

where*w^2 = -(1/4)*mu^2*k^4+mu*k^2*A^2

"How can we solve differntial equation*(1) on Maple"?""


Download dsol.mw

Why the expression of lambda[1] is too large? One of the possible values of lambda[1] should be "sqrt(1/(4*omega^2 - 4))*a[-1]". 


Why is the Maple giving this error. See attched file. Further, how can we eq. of the form "A+B`*sqrt(C) = 0" by eliminating the common denominator.


Why Maple returns empty solution (see eq. (5))? Also, is it possible that Maple not only gives us the explit solution but also the solution steps?


with(PDEtools, TWSolutions, declare)

[TWSolutions, declare]


with(DEtools, diff_table)



U := diff_table(u(x, t))

table( [(  ) = u(x, t) ] )


sys := {U[]*U[x]+U[t]-pU[x, x]+qU[x, x, x] = 0}

{u(x, t)*(diff(u(x, t), x))+diff(u(x, t), t)-pU[x, x]+qU[x, x, x] = 0}


TWS_sol := TWSolutions(sys)


map(pdetest, [TWS_sol], sys)




Download twsol.mw

How can we determine the highest (or peak) value for every hump and at what value of (x, t) in the plot?


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