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How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax.?

κ=0.2; xmax=10;

eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3};
eq2={a''[x] == a[x] f[x]^2};
boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};

An attempt to use NDSolve with the shooting method didn't work.

How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax.

κ=0.2; xmax=10;

eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3};
eq2={a''[x] == a[x] f[x]^2};
boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};

An attempt to use NDSolve with the shooting method didn't work.

How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax?

κ=0.2; xmax=10;

eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3};
eq2={a''[x] == a[x] f[x]^2};
boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};

An attempt to use NDSolve with the shooting method didn't work.

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How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax.

\[Kappa]=0κ=0.2; xmax=10;

eq1={1/\[Kappa]^2κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3};
eq2={a''[x] == a[x] f[x]^2};
boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};

An attempt to use NDSolve with the shooting method didn't work.

How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax.

\[Kappa]=0.2; xmax=10;

eq1={1/\[Kappa]^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3};
eq2={a''[x] == a[x] f[x]^2};
boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};

An attempt to use NDSolve with the shooting method didn't work.

How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax.

κ=0.2; xmax=10;

eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3};
eq2={a''[x] == a[x] f[x]^2};
boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};

An attempt to use NDSolve with the shooting method didn't work.

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