@Kitonum how to get continuous system from dicrete system by sending h (lattice parameter along x-axis) approaches to zero in maple? i.e., in the attached worksheet, if we send h --> 0, then eq (5) reduces to q_{xt} + (2r)r_{x}=0. How to do that in maple?

CD_new.mw

@Kitonum D₂ is the derivative?

@Carl Love very nice explanation. To understand completely I need more details on "order", "digits" and "degree". 

@acer lambda is also complex. I put it on maple and got the result. But one paoint is that maple do not cancel some terms in exponent i.e., "exp((1/2*I)*(-2*lambda*x+conjugate((lambda^2*x+2*t)/lambda)+conjugate((lambda^2*x-2*t)/lambda)))", you can see that "t" part should cancen each other but don't perform it. Also I used "with(PDEtools);
with(LinearAlgebra);
" in the worksheet. But you have used only "kernelopts(version);" in it. Why?simplificationCL18mod.mw

@Carl Love Its work. Further I want to compact and simplify the expression as much as possible. I tried it but can't get the simplest expression. simplification.mw

@Axel Vogt What is MultiSeries? Can you push a bit?

@Christian Wolinski  Please upload maple sheet

@Kitonum Also I want to calculate partial derivative not ordinary derivative

@Kitonum Physics:-diff is different from diff() command?

@acer Its really nice, but I am confuse how do you define R1,R2,R3 and R4. Can you briefly explain it, if possible

@Christian Wolinski Can you submit the derivation?

@Kitonum My maple gives only the first answer, but not gives the answer as given in brackets.

If we have lambda1=a1+ib1 and lambda2=a2+ib2, then what would be the above expression?

@vv lamba is a parameter and i is imaginary, so we cannot assign unique value. I am looking for and explicit expressions for solvong variable u1(x,t) and u2(x,t).

Can you provide me explicit form of these solutions?

@mmcdara

Can you provide me the explicit solutions?