Asymptotic behavior of nonlinear wave systems integrated by the method of the inverse scattering problem
Abstract
The paper considers the problem of determining the asymptotic form of the 'nonsoliton' part of solutions to systems of nonlinear wave equations. It is shown how the 'nonsoliton' asymptotic form for different integrated systems of nonlinear wave equations can be obtained by standard techniques, especially by solving the problem of parametric resonance with a linear change in perturbation frequency. Two variants of this technique are outlined: one employing the direct scattering problem for the 'integrating' operator and another based on the equations of the inverse scattering problem. The direct scattering problem is used to compute asymptotic forms for the nonlinear Schroedinger equation in the cases of wavepacket propagation in selffocusing and defocusing media. The same technique is employed to determine the asymptotic form for the Kortewegde Vries equation. The technique based on the inverse scattering equations is used to compute the asymptotic form of the sineGordon equations.
 Publication:

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki
 Pub Date:
 July 1976
 Bibcode:
 1976ZhETF..71..203Z
 Keywords:

 Asymptotic Methods;
 Nonlinear Equations;
 Schroedinger Equation;
 Wave Equations;
 Differential Equations;
 Integral Equations;
 Scattering;
 Self Focusing;
 Wave Packets;
 Physics (General)