D

The given equation is \( \vec{\phi}(x,t) = \hat{j} \sin\left(\frac{2\pi}{\lambda} vt\right) \cos\left(\frac{2\pi}{\lambda} x\right) \).

1. **Identify the Structure of the Wave**: The equation can be rewritten as a product of two parts: a sine function in time and a cosine function in space.
2. **Understanding Terms**: In this case:
- The sine term, \( \sin(2\pi vt / \lambda) \), indicates a time-dependent part, while the cosine term, \( \cos(2\pi x / \lambda) \), describes a spatial part.
3. **Stationary Wave Characteristic**: The presence of both sine and cosine components suggests interference, which is characteristic of a stationary wave.
4. **Determine Wave Type**: A stationary wave does not propagate energy through space but instead has nodes and antinodes where the wave oscillates. The presence of the sine function indicates a transverse aspect since the wave has a direction perpendicular to the wave's propagation.
Therefore, the equation represents a **Transverse stationary wave**.
Consequently, the correct answer is D.