Abstract:
A very simple exact analytic solution of the nonlinear Schrödinger equation is found in the class of periodic solutions. It describes the time evolution of a wave with constant amplitude on which a small periodic perturbation is superimposed. Expressions are obtained for
the evolution of the spectrum of this solution, and these expressions are analyzed qualitatively. It is shown that there exists a certain class of periodic solutions for which the real and imaginary parts are linearly related, and an example of a one-parameter family of
such solutions is given.
Citation:
N. N. Akhmediev, V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation”, TMF, 69:2 (1986), 189–194; Theoret. and Math. Phys., 69:2 (1986), 1089–1093
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