The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation
- 1 February 1979
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 60 (1) , 43-58
- https://doi.org/10.1002/sapm197960143
Abstract
A detailed analysis is given to the solution of the cubic Schrödinger equation iqt + qxx + 2|q|2q = 0 under the boundary conditions as |x|→∞. The inverse‐scattering technique is used, and the asymptotic state is a series of solitons. However, there is no soliton whose amplitude is stationary in time. Each soliton has a definite velocity and “pulsates” in time with a definite period. The interaction of two solitons is considered, and a possible extension to the perturbed periodic wave [q(x + T,t) = q(x,t) as |x|→∞] is discussed.Keywords
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