In here i did try my best and my equation outcome are ok but is not same as author did i dont know why, beside this he try to use two ode for constructing  a new ode which find of one solution of this can be the third solution of ode!
 i have to use eq(5) for my orginal ode  but eq(5) contain f(x) and g(x) which by some assumption  and taking two other ode eq(6) and eq(7)  they construct new one which is eq(14) and by f(xi) and g(xi) have corelation with W(xi) which is third ode  as in eq(9) and eq(11) mentioned, i try to use the solution which author mentioned but is not give me solution of third ode by using corelation what is problem here? also in eq(21)  and eq(25) when thus parameter are satisfy must our odetest be zero

i will update two maple file which realted separatly for constructing  equations and other is for apply and satisfy the solution for ode!

F-p.mw

ode-17.mw

 a while ago there is a code for changing function from trig to hyperbolic and viceversa  but i can't find that code except changind xi=I*xi there is another one?

Download convert.mw

Dear MaplePrimes Community,

With the rapid advancement of technology, it has become increasingly important to improve our workflows and reduce repetitive manual tasks. In my research, I frequently use Maple to solve  PDEs and obtain analytical solutions. However, one major difficulty I face is the time-consuming process of manually converting each result into LaTeX format.

In many cases, Maple produces multiple solutions, and I must copy and convert each one individually into LaTeX. This process is tedious, inefficient, and prone to formatting errors.

Therefore, I would like to ask:

Is it possible to establish an automated link or workflow between Maple and LaTeX such that, after solving a problem in Maple, all resulting expressions are automatically exported and inserted into a LaTeX document in the desired format and location?

Ideally, I am looking for a system where:

• Maple solutions are automatically converted into LaTeX code,

• The equations are directly placed into a specified LaTeX file or section,

• The process works for multiple solutions without manual intervention.

Furthermore, if such integration is possible, can this idea be extended to connect Maple with multiple tools (for example, Maple → LaTeX → plotting or document-generation systems), creating a more advanced automated workflow?

I would greatly appreciate any guidance, examples, or best practices for implementing such a system.

Thank you very much for your help.

Hello everyone, I am trying to reproduce Equation (25) from the paper by E. Yomba (Chaos, Solitons and Fractals, 2006) using Maple, where the improved extended algebraic Fan method is applied to the (2+1)-dimensional Broer–Kaup–Kupershmidt (BKK) system. Starting from the system in Eq. (23) and the ansatz given in Eq. (24), together with the auxiliary equation (Eq. (3)), the paper states that substituting these expressions and setting coefficients of powers of G(ξ) to zero leads to an overdetermined system whose solution yields Eq. (25). My difficulty is implementing this process in Maple: specifically, how to correctly substitute the ansatz into the PDE system, expand and collect terms with respect to G(ξ) and its derivatives, systematically extract the resulting algebraic/PDE system, and solve it efficiently (possibly using packages like PDEtools). I would appreciate guidance or example workflows for performing this type of symbolic derivation in Maple.

F1.mw

I am studying a nonlinear wave equation and trying to reproduce the energy balance method shown in a research paper. First, the original partial differential equation is reduced to an ordinary differential equation using a traveling wave transformation. After obtaining the reduced equation, the paper rewrites it in a form suitable for the energy balance method and derives the corresponding variational principle and Hamiltonian invariant. Then a trial periodic solution in cosine form is assumed. Using the Hamiltonian invariant and some initial conditions, the parameters of the trial function are determined and a periodic solution is obtained.

I would like to know how to implement this procedure in Maple. Specifically,  compute the Hamiltonian invariant from the equation, substitute the cosine trial function, and determine the unknown parameter in the trial solution using the energy balance method. I will attach images from the paper that show the derivation steps I am trying to reproduce. Any guidance on how to perform these symbolic steps in Maple would be very helpful.

f-s.mw