This section is devoted to introducing the basic concepts for wave propagation, which provides a working area of the soliton research. The summary and perspectives are presented in section 5. The existence of nuclear soliton is discussed in section 4. The general definition of solitary wave and soliton is shown in section 3. The basic concepts of wave propagation are introduced in section 2. In particular, the well-preserved nuclear matter is expected to be used for the reduction of nuclear waste by the nuclear transmutation, with the extremely high intensity/density projectile of reactions, which is not only to make a high intensity/density beam but also high projectile-density matter in the nuclear reactor. As the conservation property of the soliton has already been utilized in the optical fiber, the preservation property of nuclear matter is expected to be utilized in the nuclear engineering for preserving and condensing a certain projectile nucleus. Perfect fluidity is also associated with the conservation of nuclear matter without the loss of any information: i.e., isentropic property arising from the time-reversal symmetry. Furthermore, perfect fluidity is associated with the dissipation property of low-energy heavy-ion collisions that has been a long standing open problem in microscopic nuclear reaction theory. Since celestial bodies consist of nuclear matter, the quantitative understandings of the nuclear soliton are able to show a new aspect of the matter/heat transportation inside the (compact) stars. Indeed, perfect fluidity leads to the conservation of the number of vortexes. Accordingly, the nuclear soliton is expected to be associated with some important physics if its existence is established. It is worth mentioning here that perfect fluidity can be rephrased as inertness in the context of reaction theory. On the other hand, the nuclear soliton is also regarded as bringing about a nuclear matter state with perfect fluidity. The soliton is a wave with both individuality and stability. In other words, as is known in nuclear physics, the motion of the nucleus at the energy order of MeV is governed by the independent nucleon motion (for example, see Ring and Schuck ). For example, the effective unit of motion for the optical soliton is the photon. Such a specific scale arises from the effective unit of motion: the nucleon degree of freedom in the case of a nuclear soliton. The nuclear soliton is found in sub-atomic femto-meter scales whose energy is at the order of MeV (mega electron volt). This fact has something to do with the size and model dependence of the two common properties. The solitons are observed in any scale, if the mathematically common property is held by the master equation.
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In particular the collectivity of many-nucleon systems has been successfully treated by the nuclear DFT with and without time-dependence (for example, see Greiner and Maruhn ). Here we employ the nuclear time-dependent density functional theory (TDDFT) in which all the above four properties are included in a self-consistent manner. In most soliton research mentioned here, the size and model dependent additional properties are not seriously considered.
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From here on, we refer simply to “soliton” for a kind of non-topological soliton. In this sense, as for the terminologies of classical and quantum field theory, what we study in this article is not similar to the topological soliton, but rather corresponds to the non-topological soliton.
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The solitons in this article are the waves stably traveling without changing shape and velocity even after collisions between waves ( Figure 1). The concept of nuclear soliton is proposed by its existence in the three-dimensional nuclear time-dependent density functional formalism.