How to model a transverse wave in Matlab (Wave Equation)

if true
  % USE POTENTIAL SOLUTION TO SCALAR WAVE EQUATION TO
% PLOT S WAVE
clear
% TIME DOMAIN
t = 0:1:500;
% WAVE VECTOR
k1 = 0.4;
k2 = 0.2;
k3 = 0.3;
% COORDINATES OF RAY (DETERMINED BY WAVE VECTOR)
x = 0:2.5:50;
y = k2/k1*x;
z = k3/k1*x;
% DIV(K,X)
KX = sum([k1*x; k2*y; k3*z]); % k.x
% OTHER WAVE PARAMETERS
A = 3; % AMPLITUDE
w = 0.1; % ANGULAR FREQUENCY
% LOOP OVER TIME STEPS
for n = 1:numel(t)

 % DISPLACEMENTS (CURL OF SCALAR POTENTIAL):
 ux = k1*A*(sin(w*t(n) - KX));
 uy = k2*A*(sin(w*t(n) - KX));
 uz = k3*A*(sin(w*t(n) - KX));

 % PLOT WAVE FOR CURRENT TIME STEP
 hold off
 plot3(x,y,z,'r-');
 hold on
 plot3(x+ux,y+uy,z+uz,'ko','markersize',4,...
 'markerfacecolor','k');
 axis equal
 axis([-10 55 -10 30 -5 40])
 xlabel('x'), ylabel('y'), zlabel('z')
 title(num2str(t(n)))
 grid on
 drawnow

end end

The current code models a longitudinal wave; a wave that oscillates along the direction of propagation.

However, I am trying to model a transverse wave, where the wave oscillates perpendicular to the direction of propagation.

u(z,t) = ∇φ(z,t) = (0,0,−ik)Aexp[i(ωt − kz)] is what dictates the longitudinal wave (z is direction of propagation)

here A (which is amplitude, defined by A = 3 in the code, is just a variable)

u(z,t) = ∇ × Ψ(z,t) = (ikAy ,−ikAx ,0)exp[i(ωt − kz)] is what dictates the transverse wave. Here, A is a vector quantity, and I am not sure how to define my previously used variable A, and split it into Ax and Ay.

Thanks for any help