Multidimensional Theta Functions - 21.9 Integrable Equations

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
21.9.E1	${\displaystyle{\displaystyle 4u_{t}=6uu_{x}+u_{xxx}}}$ 4u_{t} = 6uu_{x}+u_{xxx}		4*u[t] = 6*u*u[x]+ u[x, x, x]	4*Subscript[u, t] == 6*u*Subscript[u, x]+ Subscript[u, x, x, x]	Skipped - no semantic math	Skipped - no semantic math	-	-
21.9.E2	${\displaystyle{\displaystyle iu_{t}=-\tfrac{1}{2}u_{xx}+|u|^{2}u}}$ iu_{t} = -\tfrac{1}{2}u_{xx}+|u|^{2}u		I*u[t] = -(1)/(2)*u[x, x]+(abs(u))^(2)* u	I*Subscript[u, t] == -Divide[1,2]*Subscript[u, x, x]+(Abs[u])^(2)* u	Skipped - no semantic math	Skipped - no semantic math	-	-
21.9.E3	${\displaystyle{\displaystyle(-4u_{t}+6uu_{x}+u_{xxx})_{x}+3u_{yy}=0}}$ (-4u_{t}+6uu_{x}+u_{xxx})_{x}+3u_{yy} = 0		- 4*u[t]+ 6*u*u[x]+ u[x, x, x][x]+ 3*u[y, y] = 0	Subscript[- 4*Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x, x, x], x]+ 3*Subscript[u, y, y] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
21.9.E4	${\displaystyle{\displaystyle u(x,y,t)=c+2\frac{{\partial}^{2}}{{\partial x}^{2}}\ln\left(\theta\left(\mathbf{k}x+\mathbf{l}y+\boldsymbol{{\omega}}t+\boldsymbol{{\phi}}\middle|\boldsymbol{{\Omega}}\right)\right)}}$ u(x,y,t) = c+2\pderiv[2]{}{x}\ln@{\Riemanntheta@{\mathbf{k}x+\mathbf{l}y+\boldsymbol{{\omega}}t+\boldsymbol{{\phi}}}{\boldsymbol{{\Omega}}}}		u(x , y , t) = c + 2*diff(ln(RiemannTheta(k*x + l*y + omega*t + phi, Omega)), [x$(2)])	Error	Missing Macro Error	Missing Macro Error	-	-