D

Step 1: Analyzing the waveform equation. The equation given is:
$$\vec{\phi}(x,t) = \hat{j} \sin\left(\frac{2\pi}{\lambda} vt\right) \cos\left(\frac{2\pi}{\lambda} x\right)$$
This equation represents a wave function where the sine term implies a time-dependent component and the cosine term represents a spatial component.
Step 2: Identifying the nature of the wave. The presence of both sine and cosine functions indicates that the wave does not propagate in one direction but exhibits characteristics of a stationary wave, where the nodes and antinodes are formed.
Step 3: Classifying the type of wave. Since it involves a spatial variation described by cosine (indicating a transverse oscillation perpendicular to the direction of wave propagation), it denotes a transverse stationary wave.
Therefore, the correct option is D.