&Assumptions = {n \[Element] Integers, m \[Element] Integers};
f[n_, x_] := Sqrt[2] Sin[n \[Pi] x]
a[n_, m_] := Function[{x, y}, (f[n, x] f[m, y] - f[n, y] f[m, x])/Sqrt[2]];
awave2 = Plot3D[Evaluate[a[1, 3][x, y]], {x, 0, 1}, {y, 0, 1},
PlotPoints -> 35,
PlotRange -> {-2.5, 3.5},
MeshFunctions -> {#3 &},
Mesh -> 10,
MeshStyle ->
Directive[ColorData["DeepSeaColors"][.1], Thickness[.002]],
ColorFunction -> "LakeColors",
BoxRatios -> {1, 1, .7},
Boxed -> False,
Axes -> False];
agroundplot = Plot3D[-3, {x, 0, 1}, {y, 0, 1},
MeshFunctions -> {a[1, 3][#1, #2] &},
Mesh -> 10,
MeshStyle ->
Directive[ColorData["DeepSeaColors"][.1], Thickness[.002]],
PlotPoints -> 50,
ColorFunction -> (ColorData["LakeColors"][(a[1, 3][#1, #2] + 2.5)/
6] &)
];
awave3 = Show[{awave2, agroundplot},
PlotRange -> {{0, 1}, {0, 1}, {-3, 3}},
Axes -> None,
PlotRangePadding -> None,
ImagePadding -> 1,
FaceGrids -> {
{{-1, 0, 0}, {Table[i, {i, 0, 1, 1/9}],
Table[i, {i, -3, 3, 1}]}},
{{0, -1, 0}, {Table[i, {i, 0, 1, 1/9}], Table[i, {i, -3, 3, 1}]}}
},
ViewPoint -> 1000 {5, 5, 2},
ViewVertical -> {0, 0, 1},
ViewCenter -> {.5, .5, 0},
ImageSize -> 600]
Export["Asymmetricwave2.png", awave3, "PNG"]