
doi: 10.1063/1.525786
In an earlier paper we established an equivalence between the dynamics of interacting sine–Gordon solitons and the motions of poles of the corresponding Hamiltonian density. In particular, we found analytic expressions for the forces acting between the solitons and used these to represent the N-soliton solution as an N-body interaction between classical particles. In this paper, we apply the methods of our previous analysis to obtain a dynamically equivalent particle representation for interacting Korteweg–de Vries solitons. The representation is faithful and a detailed analysis is present for the one- and two-soliton solutions. In these cases the particle motions accurately reflect the behavior of the solitons, giving, respectively, a uniform motion and a repulsive interaction. Furthermore, in the case of the two-soliton solutions, the phase shifts calculated from the particle trajectories are the same as those obtained from an asymptotic analysis of the waveforms. Because of the nature of the Korteweg–de Vries equation, there are important differences between the present analysis and that employed for the sine–Gordon equation and these are discussed in some detail. A comparison with related work on other solutions of the Korteweg–de Vries is also presented.
classical many-body problems with two-body forces, duality between fields, Partial differential equations of mathematical physics and other areas of application, Constructive quantum field theory, nonlinear evolution equations, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, particle representation, Korteweg-de Vries solitons, kinematics of the poles
classical many-body problems with two-body forces, duality between fields, Partial differential equations of mathematical physics and other areas of application, Constructive quantum field theory, nonlinear evolution equations, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, particle representation, Korteweg-de Vries solitons, kinematics of the poles
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