Soliton solutions of the negative-order nonlinear Schrödinger equation
G. U. UrazboevKhorezm Branch of the Romanovsky Institute of Mathematics, Uzbekistan Academy of Science, Urgench, UzbekistanIroda Ismailovna BaltaevaUrgench State University, Urgench, UzbekistanA. K. BabadjanovaKhorezm Branch of the Romanovsky Institute of Mathematics, Uzbekistan Academy of Science, Urgench, Uzbekistan
ABI
Abstract
We discuss the integration of the Cauchy problem for the negative-order nonlinear Schrödinger equation in the class of rapidly decreasing functions via the inverse scattering problem method. In particular, we obtain the time dependence of scattering data of the Zakharov–Shabat system with the potential that is a solution of the considered problem. We give an explicit representation of the one-soliton solution of the negative-order nonlinear Schrödinger equation based on the obtained results.
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