If

p_{x} = a*p + u*q;    (1)

q_{x} = -conjugate(u)*p - a*q;  (2)     # where a is complex parameter, p_{x} mean derivative of p w.r.t x

Define, u=p^2+conjugate(q)^2,  (3)  

Now take the derivative of (3) w.r.t x and by using (1) and (2), we get

 u_{x}=2(a*p^2 - conjugate(a)*conjugate(q)^2) + 2*(p^2 + conjugate(q)^2)*(p*q - conjugate(p)*conjugate(q)).  (4)

How to calculate the results (4) on maple?

123.mw

I want to calculate (partialH/partialq). But I encountered an error when I evaluate it.

restart;
with(PDEtools);
with(linalg);
alias(q = q(x, t), p = p(x, t));
                              q, p
H := lambda*p*q+conjugate(lambda)*conjugate(p)*conjugate(q)+(1/2*(p^2+conjugate(q)^2))*(conjugate(p)^2+q^2);
                                      
diff(H, q(x, t));

maple shows error:

Error, invalid input: diff received q(x, t), which is not valid for its 2nd argument
How to fix this issue?

I am trying to solve 4x4 determinants, but there is many determinants in my problem, I want to solve it in maple. Maple gives the answer but its expression is large. how to confine large expression in a nice simple form in maple? Here is an example:

with(LinearAlgebra):

A:=Matrix([[phi,conjugate(psi),chi,conjugate(rho)],[psi,-conjugate(phi),rho,-conjugate(chi)],[lambda1*phi,conjugate(lambda1)*conjugate(psi),lambda2*chi,conjugate(lambda2)*conjugate(rho)],[lambda1*psi,-conjugate(lambda1)*conjugate(phi),lambda2*rho,-conjugate(lambda2)*conjugate(chi)]]);

I am trying to solve a set of differential equations in maple. The maple code:

de1:=diff(u1(x,t),x)=-h*(u1(x,t))+i*exp(-i*t)*(u2(x,t));
              d
       de1 := -- u1(x, t) = -h u1(x, t) + i exp(-i t) u2(x, t)
              dx

> de2:=diff(u1(x,t),t)=(-h-i/2)*u1(x,t)-h*exp(-i*t)*u2(x,t);

         d
  de2 := -- u1(x, t) = (-h - 1/2 i) u1(x, t) - h exp(-i t) u2(x, t)
         dt

> dsolve({de1,de2},{u1(x,t),u1(x,t)});
 

However, when I execute it, maple show "Warning: system is consistent". How to remove it

I am trying to solve system of coupled equations in maple, but when I execute it, maple gives a trivial answer. Here is the code:

de1:=diff(u1(x,t),x)=(i/lambda)*(p*u1(x,t)+q*u2(x,t));
                  d             i (p u1(x, t) + q u2(x, t))
           de1 := -- u1(x, t) = ---------------------------
                  dx                      lambda

> de2:=diff(u2(x,t),x)=(i/lambda)*(q*u1(x,t)-p*u2(x,t));

                  d             i (q u1(x, t) - p u2(x, t))
           de2 := -- u2(x, t) = ---------------------------
                  dx                      lambda

> de3 := diff(u1(x,t),t) = -(i*lambda/2)*u1(x,t)-q*u2(x,t);

             d
      de3 := -- u1(x, t) = - 1/2 i lambda u1(x, t) - q u2(x, t)
             dt

> de4 := diff(u2(x,t),t) = 1/2*i*lambda*u2(x,t)+q*u1(x,t);

              d
       de4 := -- u2(x, t) = 1/2 i lambda u2(x, t) + q u1(x, t)
              dt

> dsolve({de1,de2,de3,de4},{u1(x,t),u2(x,t)});