Question: How to solve simultaneous partial differential equations analytically.

Please how can i obtain analytical siolution of the system of pde with maple

pde1 := diff(u(x, t), t) = (1/50)*(diff(u(x, t), x, x))+1-4*u(x, t)+u(x, t)^2*v(x, t);
pde2 := diff(v(x, t), t) = (1/50)*(diff(v(x, t), x, x))+3*u(x, t)-u(x, t)^2*v(x, t);
u(x, 0) = 1+sin(2*Pi*x), v(x, 0) = 3, u(0, t) = u(1, t) and u(1, t) = 1, v(0, t) = v(1, t) and v(1, t) = 3;


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