Painlevé Transcendents - 32.13 Reductions of Partial Differential Equations

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
32.13.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v_{t}-6v^{2}v_{x}+v_{xxx} = 0}
v_{t}-6v^{2}v_{x}+v_{xxx} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
v[t]- 6*(v)^(2)* v[x]+ v[x, x, x] = 0
 
Subscript[v, t]- 6*(v)^(2)* Subscript[v, x]+ Subscript[v, x, x, x] == 0
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x(3t)^{-1/3}}
z = x(3t)^{-1/3}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(x(+)*y*I) = (x(3*t))^(- 1/3)
 
(x[+]*y*I) == (x[3*t])^(- 1/3)
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v(x,t) = (3t)^{-1/3}w(z)}
v(x,t) = (3t)^{-1/3}w(z)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
v(x , t) = (3*t)^(- 1/3)* w*((x + y*I))
 
v[x , t] == (3*t)^(- 1/3)* w*((x + y*I))
 Skipped - no semantic math Skipped - no semantic math - -
32.13.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{t}+6uu_{x}+u_{xxx} = 0}
u_{t}+6uu_{x}+u_{xxx} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
u[t]+ 6*u*u[x]+ u[x, x, x] = 0
 
Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x, x, x] == 0
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x(3t)^{-1/3}}
z = x(3t)^{-1/3}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(x(+)*y*I) = (x(3*t))^(- 1/3)
 
(x[+]*y*I) == (x[3*t])^(- 1/3)
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x+3\lambda t^{2}}
z = x+3\lambda t^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(x + y*I) = x + 3*lambda*(t)^(2)
 
(x + y*I) == x + 3*\[Lambda]*(t)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(x,t) = W(z)-\lambda t}
u(x,t) = W(z)-\lambda t		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
u(x , t) = W*((x + y*I))- lambda*t
 
u[x , t] == W*((x + y*I))- \[Lambda]*t
 Skipped - no semantic math Skipped - no semantic math - -
32.13.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{xt} = \sin@@{u}}
u_{xt} = \sin@@{u}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
u[x, t] = sin(u)

Subscript[u, x, t] == Sin[u]
Failure Failure
Failed [300 / 300]
Result: .70450695e-2+.1624035369*I
Test Values: {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, u[x*t] = 1/2*3^(1/2)+1/2*I}


Result: -1.358980334+.5284289409*I
Test Values: {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, u[x*t] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[0.007045069484300837, 0.16240353677712993]
Test Values: {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[u, Times[t, x]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-1.3589803343001376, 0.5284289405615687]
Test Values: {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[u, Times[t, x]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
32.13#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = xt}
z = xt		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(x + y*I) = x*t
 
(x + y*I) == x*t
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(x,t) = v(z)}
u(x,t) = v(z)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
u(x , t) = v*((x + y*I))
 
u[x , t] == v*((x + y*I))
 Skipped - no semantic math Skipped - no semantic math - -
32.13.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{tt} = u_{xx}-6(u^{2})_{xx}+u_{xxxx}}
u_{tt} = u_{xx}-6(u^{2})_{xx}+u_{xxxx}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
u[t, t] = u[x, x]- 6*(u)^(2)[x, x]+ u[x, x, x, x]
 
Subscript[u, t, t] == Subscript[u, x, x]- 6*Subscript[(u)^(2), x, x]+ Subscript[u, x, x, x, x]
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x-ct}
z = x-ct		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(x + y*I) = x - c*t
 
(x + y*I) == x - c*t
 Skipped - no semantic math Skipped - no semantic math - -
32.13#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(x,t) = v(z)}
u(x,t) = v(z)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
u(x , t) = v*((x + y*I))
 
u[x , t] == v*((x + y*I))
 Skipped - no semantic math Skipped - no semantic math - -
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