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GERF

Symbols

  • BalanceConstant
  • GERFSolve
Taggar`GERF`
BalanceConstant
​
BalanceConstant[eqn,u[x,t]]
calculates the balancing constant of given
eqn
in
u[x,t]
.
​
​
BalanceConstant
[{
eqn
1
,
eqn
2
,...,
eqn
k
},{
u
1
[vars],
u
2
[vars],...,
u
k
[vars]}]
calculates the balancing constant of given
{
eqn
1
,
eqn
2
,...,
eqn
k
}
in
{
u
1
[vars],
u
2
[vars],...,
u
k
[vars]}
.
​
Examples  
(3)
Basic Examples  
(2)
This is the Burgers' equation in
(1+1)
-dimensions:
In[1]:=
burgers=
∂
t
u[x,t]+u[x,t]
∂
x
u[x,t]-ν
∂
x,x
u[x,t]0
Out[1]=
(0,1)
u
[x,t]+u[x,t]
(1,0)
u
[x,t]-ν
(2,0)
u
[x,t]0
Its balance constant:
In[2]:=
BalanceConstant
[burgers,u[x,t]]
Out[2]=
1
​
Another example, Calogero–Bogoyavlenskii–Schiff equation in
(2+1)
-dimensions:
In[1]:=
cbs=
∂
x,t
u[x,y,t]+4
∂
x
u[x,y,t]
∂
x,y
u[x,y,t]+2
∂
x,x
u[x,y,t]
∂
y
u[x,y,t]+
∂
x,x,x,y
u[x,y,t]0;
In[2]:=
BalanceConstant
[cbs,u[x,y,t]]
Out[2]=
1
Scope  
(1)

SeeAlso
GERFSolve
""

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