<< Graphics`Arrow`

1D Analitic kink

a =  .2;  l = {Hue[ .6]};  
    f0 = 0;
For[x = -5, x < 5, 
        x +=  .5, 
f = 
          4 ArcTan[Exp[x]] + f0; 
dy = a Cos[f];  
        dx = a Sin[f]; 
l = 
          Append[l, 
            Arrow[{x - dx, -dy}, {x + dx, dy}, 
              HeadLength ->  .1 a]];
];
Show[Graphics[l],AspectRatio -> .04];

1D kink "relaxation"

m = Table[0, {10}];  m[[10]] = π;  
    h2 =  .1;
For[it = 0, 
      it < 100,  it++, 
For[i = 2, 
        i < 10, i++, 
m[[i]] = (m[[i - 1]] + 
                m[[i + 1]] - h2 Sin[m[[i]]])/
            2]
]

a =  .45;  l = {Hue[ .6]};  
    f0 = 0;
For[i = 1, 
        i < 11, i++, 
f = m[[i]] + f0; 
        dy = a Cos[f];  
        dx = a Sin[f]; 
l = 
          Append[l, 
            Arrow[{i - dx, -dy}, {i + dx, dy}, 
              HeadLength ->  .05 a]];
];
Show[Graphics[l],AspectRatio -> .1];

2D vortex-kink-antivortex

nx = 15; ny = 30; h2 =  .1;
m = Table[0, {nx}, {ny}];
For[i = 7, i < 23, i++, m[[nx, i]] = π]

For[it = 0, 
      it < 100, it++, 
For[i = 2, 
        i < nx, i++, 
For[j = 2, 
          j < ny, j++, 
m[[i, 
                  j]] = (m[[i - 1, j]] + m[[i + 1, j]] + 
                    m[[i, j - 1]] + m[[i, j + 1]] - 
                    h2 Sin[m[[i, j]]])/
                4;
]
]
]

a =  .4; da =  .015;  l = {Hue[ .6]};  
    f0 = Pi/2;
For[j = 1, 
        j ≤ ny, j++, 
For[i = 1, 
          i < nx, i++, 
f = m[[i, j]] + f0; 
          dy = a Cos[f];  
          dx = a Sin[f]; 
l = 
            Append[l, 
              Arrow[{i - dx, j - dy}, {i + dx, j + dy}, 
                HeadLength -> 
                  da]]; 
f = -m[[i, j]] + f0; 
          dy = a Cos[f];  
          dx = a Sin[f]; 
l = 
            Append[l, 
              Arrow[{2 nx - i - dx, j - dy}, {2 nx - i + dx, j + dy}, 
                HeadLength -> 
                  da]];
]; 
f = 
          m[[nx, j]] + f0; dy = a Cos[f];  
        dx = a Sin[f]; 
l = 
          Append[l, 
            Arrow[{nx - dx, j - dy}, {nx + dx, j + dy}, 
              HeadLength -> 
                da]];
];
Show[Graphics[l],AspectRatio -> 1];