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These are questions asked by Ahmed111

How can we draw the pot function the same as in the attached figure (namely 'pot.png')? The values of V(x) may not be the same.


dchange gives the error when I try to convert pde into ode. Why?



pde1 := diff(u(x, t), t)-(diff(u(x, t), `$`(x, 2), t))+3*u(x, t)^2*(diff(u(x, t), x))-2*(diff(u(x, t), x))*(diff(u(x, t), `$`(x, 2)))-u(x, t)*(diff(u(x, t), `$`(x, 3))) = 0

diff(u(x, t), t)-(diff(diff(diff(u(x, t), t), x), x))+3*u(x, t)^2*(diff(u(x, t), x))-2*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x))-u(x, t)*(diff(diff(diff(u(x, t), x), x), x)) = 0


trans1 := {seq(var[i] = tau[i], i = 2), FN = Y(zz), var[1] = (zz-(sum(lambda[i]*tau[i], i = 2)))/lambda[1]}

{FN = Y(zz), var[1] = (-lambda[2]*tau[2]+zz)/lambda[1], var[2] = tau[2]}


ode1 := dchange(trans1, pde, [Y(zz), zz, seq(tau[i], i = 2)])

Error, (in dchange/info) the number of new and old independent variables must be the same. Found {zz, tau[2]} as new, while {FN, var[1], var[2]} as old



diff(u(x, t), t), -(diff(diff(diff(u(x, t), t), x), x)), 3*u(x, t)^2*(diff(u(x, t), x)), -2*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x)), -u(x, t)*(diff(diff(diff(u(x, t), x), x), x))



Download P_O.mw

I solved the differential equation using 'dsolve' and Maple returns it with fiver possible solutions. How can we get the single possible solution for w(x) if we assume c, g (constants) are positive? Also, can we convert JacobiSN() to a simple trigonometric or algebraic function?




q := (1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0

(1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0


dsolve((1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0, {w(x)})

w(x) = (2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = (-2*(c^2+2*g)^(1/2)+2*c)^(1/2), w(x) = -(2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = -(-2*(c^2+2*g)^(1/2)+2*c)^(1/2), w(x) = 2*JacobiSN((1/2)*(-2*c+2*(c^2+2*g)^(1/2))^(1/2)*x+_C1, ((c*(c^2+2*g)^(1/2)-c^2-g)*g)^(1/2)/(c*(c^2+2*g)^(1/2)-c^2-g))*g/(g*(-c+(c^2+2*g)^(1/2)))^(1/2)




Download solve.mw

How to linearize eq (6) by neglecting all higher order terms i.e., epsilon[1]^2, epsilon[2]^2, epsilon[1]*epsilon[2]... etc? How to do it in maple?


Can we write v matrix in terms of matrix u? i.e., v=const*u.


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