Dynamics of sine-Gordon solitons in the presence of perturbations

Experimental characterization of a quantum many-body system via higher-order correlations

“…This characterises the essential features of the system, the relevant quasiparticles, their interactions and possible topologically distinct vacua. We verify that in thermal equilibrium the physics can be described by the quantum sine-Gordon model [3][4][5][6], relevant for a wide variety of disciplines from particle to condensed-matter physics [7][8][9]. Our experiment establishes a general method to analyse quantum many-body systems in experiments.…”

Physical dynamics of quasi-particles in nonlinear wave equations

“…Unfortunately, there is no general agreement on the matter, and the center of a coherent structure (e.g., a soliton) has to be defined on a case-bycase basis. A definition is given by Bergman et al [26] but, as Kaup [27] shows, depending upon the definition being used, one may obtain that the quasi-particle's dynamics are Newtonian [20] or non-Newtonian [21] clearly, this is quite a discrepancy. In this respect, the closest work to ours is that of Rice [18], who derives the discrete Hamiltonian and Lagrangian for a single quasi-particle whose support can be considered an internal parameter of the problem.…”

“…For example, in order to establish the effects of acceleration on the shape of the SGE's solitons, Fogel et al [20] introduced a driving force into the SGE. However, this required also adding dissipation in the field equation in order to stabilize the evolution of the solitons, i.e., to ensure that they reach a steady terminal velocity [20,21]. Adding dissipation opens new horizons of investigation, and different physical mechanisms can be considered as progenitors of the dissipative force.…”

Complete eigenfunctions of linearized integrable equations expanded around a soliton solution

“…For linearization around singlesoliton solutions, these complete eigenfunctions have been obtained for a large class of integrable equations, such as the KdV hierarchy, NLS hierarchy, modified-KdV hierarchy, sine-Gordon, and Benjamin-Ono equations [2][3][4][5][6][7][8][9]. It has been found that these eigenfunctions are related to squared eigenfunctions of the associated eigenvalue problem (except for the Benjamin-Ono equation).…”