Solitons use a combination of nonlinearity and dispersion to propagate pulses along a 1-D channel whose *shape is preserved*. Standard solitons "simply" pass through one another "unaltered in shape, amplitude, or velocity" (see link below). Are there weird equations and soliton solutions that attempt to preserve the "holes" between them -- i.e., in addition to preserving the shape of the pulse itself, the medium would also attempt to preserve the *space between pulses*, so that they would settle down into an orderly pulse train? ---- https://arxiv.org/abs/1407.5087 Collisions of matter-wave solitons "Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass through one another and emerge from the collision unaltered in shape, amplitude, or velocity. This remarkable property is mathematically a consequence of the underlying integrability of the one-dimensional (1D) equations, such as the nonlinear Schr\"odinger equation, that describe solitons in a variety of wave contexts, including matter-waves$^{1,2}$. Here we explore the nature of soliton collisions using Bose-Einstein condensates of atoms with attractive interactions confined to a quasi-one-dimensional waveguide. ..."