Topological solitons are non-perturbative configurations in nonlinear field theories, such as kinks, vortices, and monopoles, which play important roles in various physical systems. This review discusses the basic properties of topological solitons using the one-dimensional kink solution of the non-integrable φ⁴ model. The model has applications in condensed matter physics, field theory, and cosmology. The kink solution is a topological non-trivial configuration that interpolates between two degenerate vacua. The dynamics of kinks, including their scattering, radiation, and annihilation, have been studied extensively. In the non-integrable φ⁴ model, kink-antikink collisions can produce various results, such as oscillating bound states or bouncing and reflecting solitons. The review discusses the perturbative fluctuations of the kink solution and the mechanism of resonant bouncing scattering. The kink solution is described by the Lagrangian of the φ⁴ model, which includes a potential with two minima. The kink solution is given by φ₀ = m/√λ tanh(mx/√2). The perturbative corrections to the kink solution are calculated using the expansion of the field in powers of ε. The corrections are described by eigenfunctions of the operator D², which include a zero mode corresponding to kink translation, a vibrational mode connected with the time-dependent deformation of the kink profile, and continuum modes corresponding to scalar particle excitations. The zero mode correction leads to a shift of the kink position, which is given by δx^(1) = -ε 3m/(2√2) t². The review also discusses the production of kink-antikink pairs in the collision of particle-like states related to resonance excitation of the oscillon configuration.Topological solitons are non-perturbative configurations in nonlinear field theories, such as kinks, vortices, and monopoles, which play important roles in various physical systems. This review discusses the basic properties of topological solitons using the one-dimensional kink solution of the non-integrable φ⁴ model. The model has applications in condensed matter physics, field theory, and cosmology. The kink solution is a topological non-trivial configuration that interpolates between two degenerate vacua. The dynamics of kinks, including their scattering, radiation, and annihilation, have been studied extensively. In the non-integrable φ⁴ model, kink-antikink collisions can produce various results, such as oscillating bound states or bouncing and reflecting solitons. The review discusses the perturbative fluctuations of the kink solution and the mechanism of resonant bouncing scattering. The kink solution is described by the Lagrangian of the φ⁴ model, which includes a potential with two minima. The kink solution is given by φ₀ = m/√λ tanh(mx/√2). The perturbative corrections to the kink solution are calculated using the expansion of the field in powers of ε. The corrections are described by eigenfunctions of the operator D², which include a zero mode corresponding to kink translation, a vibrational mode connected with the time-dependent deformation of the kink profile, and continuum modes corresponding to scalar particle excitations. The zero mode correction leads to a shift of the kink position, which is given by δx^(1) = -ε 3m/(2√2) t². The review also discusses the production of kink-antikink pairs in the collision of particle-like states related to resonance excitation of the oscillon configuration.