Distribution of solitons from nonlinear integrable equations

Details Distribution of solitons from nonlinear integrable equations Distribution of solitons from nonlinear integrable equations

May 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrva..39.5289p&link_type=abstract

Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 39, May 15, 1989, p. 5289-5298. Research supported by the

Physics

General Physics

6

Inverse Scattering, Nonlinear Equations, Schroedinger Equation, Solitary Waves, Eigenvalues, Korteweg-Devries Equation

Scientific paper

The class of nonlinear equations which can be integrated by the method of inverse scattering transforms is investigated. The analysis of Karpman and Sokolov (1968) for the Korteweg-de Vries equations is extended to the equations for the standard Zakharov-Shabat eigenvalue problem with complex discrete spectrum. The soliton distribution function is obtained as a functional of the initial conditions, and it is shown that the distributions of the real and imaginary parts of the eigenvalues for the continuous case are in good agreement with those determined by other methods. The applicability of the present approach to the nonlinear or derivative nonlinear Schroedinger equations is discussed.

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