Soliton solutions of the negative-order nonlinear Schrödinger equation
G. U. Urazboev, Iroda Ismailovna Baltaeva, A. K. Babadjanova
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.
Topics & Concepts
SolitonNonlinear Schrödinger equationNonlinear systemMathematical physicsPhysicsOrder (exchange)MathematicsMathematical analysisApplied mathematicsQuantum mechanicsFinanceEconomicsNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Mathematical Physics Problems