A soleakon is a nonlinear self-trapped localized wave that induces a waveguide through the nonlinearity and populates its slowly-attenuating leaky mode, self-consistently and robustly. Leaky modes are localized in, or in the vicinity of, the waveguide, but unlike guided modes that decay exponentially outside the waveguide, leaky modes remain oscillatory, indicating the outgoing flow of energy to the cladding. During propagation, the localized power in a leaky mode gradually leaks out to the continuum. Soleakons and their self-induce waveguides are non-stationary because they continuously leak power to the continuum up to the abrupt soleakon disintegration where the soleakon power reaches a low threshold power. A soleakon  propagation distance should be much larger than the diffraction length of the beam

under linear propagation conditions. Otherwise, the beam will not exhibit particle-like features such as collisions and it therefore cannot be called a soleakon. Up to my  work, soleakons were predicted in two geometries:

1) Homogenous media with a combination of nonlocal self-defocusing and kerr

self-focusing nonlinearities.

2) Array of slab waveguides with either a combination of nonlocal self-

defocusing and local self-focusing nonlinearities or a local saturable self-

focusing nonlinearity.

In this thesis, I propose bright soleakons that are solely supported by self-defocusing nonlinearity. I demonstrate numerically scalar bell (fundamental) and dipole soleakons, as well as multi-mode vector soleakons. I found that the threshold power  for disintegration of the dipole soleakon is much larger than the threshold  disintegration power of the bell soleakon. In the bell-dipole vector soleakon case, the  two fields interact through the nonlinearity causing the vector soleakon to disintegrate  collectively when it components joint power reaches a threshold value that is between  the threshold power for the scalar fundamental and dipole soleakons.