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Stability of exact solutions of the nonlinear Schrödinger equation in an external potential having supersymmetry and parity-time symmetry

Cooper, Fred ; Khare, Avinash ; Comech, Andrew ; Mihaila, Bogdan ; Dawson, John F ; Saxena, Avadh

Journal of physics. A, Mathematical and theoretical, 2017-01, Vol.50 (1), p.15301 [Periódico revisado por pares]

United States: IOP Publishing

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  • Título:
    Stability of exact solutions of the nonlinear Schrödinger equation in an external potential having supersymmetry and parity-time symmetry
  • Autor: Cooper, Fred ; Khare, Avinash ; Comech, Andrew ; Mihaila, Bogdan ; Dawson, John F ; Saxena, Avadh
  • Assuntos: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; dynamical system ; MATHEMATICS AND COMPUTING ; nonlinear Schrödinger equation ; PT symmetry ; soliton stability ; supersymmetry
  • É parte de: Journal of physics. A, Mathematical and theoretical, 2017-01, Vol.50 (1), p.15301
  • Notas: JPhysA-105758.R1
    USDOE Laboratory Directed Research and Development (LDRD) Program
    LA-UR-16-22361
    89233218CNA000001
  • Descrição: We discuss the stability properties of the solutions of the general nonlinear Schrödinger equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time (   ) symmetric superpotential W ( x ) that we considered earlier, Kevrekidis et al (2015 Phys. Rev. E 92 042901). In particular we consider the nonlinear partial differential equation { i ∂ t + ∂ x 2 − V − ( x ) + ( x , t ) 2 κ } ( x , t ) = 0 , for arbitrary nonlinearity parameter κ. We study the bound state solutions when V − ( x ) = ( 1 / 4 − b 2 ) sech 2 ( x ) , which can be derived from two different superpotentials W ( x ) , one of which is complex and   symmetric. Using Derrick's theorem, as well as a time dependent variational approximation, we derive exact analytic results for the domain of stability of the trapped solution as a function of the depth b2 of the external potential. We compare the regime of stability found from these analytic approaches with a numerical linear stability analysis using a variant of the Vakhitov-Kolokolov (V-K) stability criterion. The numerical results of applying the V-K condition give the same answer for the domain of stability as the analytic result obtained from applying Derrick's theorem. Our main result is that for κ > 2 a new regime of stability for the exact solutions appears as long as b > b crit , where b crit is a function of the nonlinearity parameter κ. In the absence of the potential the related solitary wave solutions of the NLSE are unstable for κ > 2 .
  • Editor: United States: IOP Publishing
  • Idioma: Inglês
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