@mmcdara I think this is not actual I am asking, I need a system of alegrabic equations from different powers of x,y,z,t and their multiple, after putting f into the bilinear equation Eq., I am unable when I put f into Eq and solve this for collect(Eq,{x,y,z,t},distributed) command because maple can not collect explicitily x,y,z,t and their products as Eq in involves JacobiCN(\xi_3,2/5) function. If, we enable to get such system, then it can be solved simultanously. 

@Rouben Rostamian  

v can be taken as free parameter, system is related to P and W in \xi, remove singularity in second equation.

Any one can help to solve this system of PDE, all information is attached in previous comments.

Real_and_Img_components.mw

Still not solved facing issue to solve the system of PDEs. Please can anyone help me to solve this system.

@dharr 7029

I have attached one more link to help for solution of this system, actually we are solving this system "Variable separation solutions" as mentioned in this link, and where q(x,y,t)=\chi(x,t)+\varphi(y), both \chi(x,t) & \variphi(y) are arbitrary function. As in given link after putting the initial solution u, they assume q(x,y,t)=\chi(x,t)+\varphi(y), then collect different powers of \phi. 

helping_note_for_solution_of_pde.pdf

@dharr 7039 I have attached another maple file in I assume result (8) and then solve the system, solution of system looks like result (7), not exactly but in terms of partial derivative of \chi with x, there should be q_x q_y (noted that q(x,y,t)=\chi(x,t)+\varphi(t) ).

Find_solution-system.mw

Dear dharr 7029,

Thank you for your effort and time, actually I am also confused to solve this system of PDEs. I have attached paper I am exploring that some part already shared, alongwidth my calculation to obtain this system (named as Find_Solution.mw).

Find_Solution.mw

Multi_Dromion-Solitoff_and_Fractal_Excitations_for_2+1)-DimensionalBoiti-Leon-Manna-Pempinelli_System.pdf