i did my try to sketch the best shape of graph by existing code but the 3D shape in matlab is not what i am looking and is  not intresting for this kind of plot so i want use and design a better shape of 3D plot for thus contour  i need help for that 

plot-help.mw

i did simplify and each time work but this time is give me another thing can anyone find what is problem?

pdetest2.mw

in here i did exactly the same but i am not sure the author did something mistake or i did becuase one term in the pde is change and how exactly do that replacement in eq62?

S.mw

i did try and even replace the function w(t) by anotehr thing but is not working  how i can find that and make be answer of my pde?

k1.mw

How can find thus parameters 

Dr.D-problem.mw