The Wave Equation: Right moving solution I

Manipulate[Plot[Sin[x-t],{x,-10,10},PlotRange->{-1,1},PlotLabel->"Right moving solution to the wave equation"],{t,-10,10}]

The Wave Equation: Left moving solution I

Manipulate[Plot[Sin[x+t],{x,-10,10},PlotRange->{-1,1},PlotLabel->"Left moving solution to the wave equation"],{t,-10,10}]

The Wave Equation : Superposition of left and right movers I to form standing wave

Manipulate[Plot[Sin[x-t]-Sin[x+t],{x,-10,10},PlotRange->{-2,2},PlotLabel->"Standing wave solution to the wave equation"],{t,-10,10}]
Manipulate[Plot[{Sin[x-t]-Sin[x+t],Sin[x-t],-Sin[x+t]},{x,-10,10},PlotRange->{-2,2},PlotLegends->{"superposition","right mover","left mover"},PlotLabel->"Standing wave (with decomposition)"],{t,-10,10}]

The Wave Equation: Right moving solution II

Manipulate[Plot[((x-t)/2)^2*Sin[x-t],{x,-20,10},PlotRange->{-110,60},PlotLabel->"Right moving solution to the wave equation"],{t,-14,20}]

The Wave Equation: Left moving solution II

Manipulate[Plot[100/Cosh[x+t],{x,-20,10},PlotRange->{-110,60},PlotLabel->"Left moving solution to the wave equation"],{t,-14,20}]

The Wave Equation : Superposition of left and right movers II

Manipulate[Plot[0.6*(((x-t)/2)^2*Sin[x-t]-100/Cosh[x+t]),{x,-20,10},PlotRange->{-110,60},PlotLabel->"Superposition of left and right moving solutions to wave equation"],{t,-14,20}]
Manipulate[Plot[{0.6*(((x-t)/2)^2*Sin[x-t]-100/Cosh[x+t]),0.6*((x-t)/2)^2*Sin[x-t],0.6*(-100/Cosh[x+t])},{x,-20,10},PlotRange->{-110,60},PlotLabel->"Superposition of left and right moving solutions (with decomposition)",PlotLegends->{"superposition","right mover","left mover"}],{t,-14,20}]

The Wave Equation: IVP solution

Manipulate[Plot[10*(Sech[x+t]+Sech[x-t])+t,{x,-100,100},PlotRange->{0,50}],{t,0,51}]