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How can I create the Maple code using exponential-function solving the equation below?

$u_t = \gamma u_x+6u(u_x)^2+(3u^2-1)u_{xx}-u_{xxxx}$

$u_t =u_{xx}-u^3+u,$

$\alpha u''(x) = \beta u(x)(u(x)-m)(u(x)-m)$

Respectively, where $\alpha , \beta , m , \gamma$ are the constants.

How can I formulate the problem into a iterative or recursive to solve it with a program?

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