Particle representation for Korteweg--de Vries solitons

Journal Article · Fri Apr 01 04:00:00 EST 1983 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525786· OSTI ID:6299161

Bowtell, G; Stuart, A E.G.

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.

• Research Organization: Department of Mathematics, The City University, Northampton Square, London EC1V OHB, England
• OSTI ID: 6299161
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 24:4; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
DUALITY
EQUATIONS
FIELD EQUATIONS
HAMILTONIANS
KORTEWEG-DE VRIES EQUATION
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SHIFT
QUANTUM OPERATORS
QUASI PARTICLES
SINE-GORDON EQUATION
SOLITONS