In some mathematical models, a particle is an excitation of a field, e.g. a mountain is an excitation of a height field. It makes calculations much easier. In those models, waves can be represented in many different ways.
In the real world, a particle can be a lot of different things, but usually we use this word to describe small parts of larger objects. There is no much physical difference between a small grain of sand and a planet, but we use different words for them, while we use the same word for small things, which can be different by many orders of magnitude.
In the real world, a wave, is just a form of group behavior of particles, i.e. many particles are doing the same thing at once because of an interaction between them and some energy in a system. For example, merging of black holes makes waves in a galaxy, so we can watch that in super slow motion.
Hopfions are promising. Hopfion model explains how waves can create a particle, so we will have full circle: particles -> waves -> particles -> waves...
In the real world, a particle can be a lot of different things, but usually we use this word to describe small parts of larger objects. There is no much physical difference between a small grain of sand and a planet, but we use different words for them, while we use the same word for small things, which can be different by many orders of magnitude.
In the real world, a wave, is just a form of group behavior of particles, i.e. many particles are doing the same thing at once because of an interaction between them and some energy in a system. For example, merging of black holes makes waves in a galaxy, so we can watch that in super slow motion.