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Title: Double-Wronskian solitons and rogue waves for the inhomogeneous nonlinear Schrödinger equation in an inhomogeneous plasma

Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us to investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed. -- Highlights: •Double-Wronskian soliton solutions are obtained and proof is finished by virtue of some double Wronskian identities. •Asymptotic analysis is applied for us to investigate the interaction between the two solitons. •First- and second-order rogue-wave solutions are constructed viamore » a generalized Darboux transformation. •Influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.« less
Authors:
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Publication Date:
OSTI Identifier:
22314797
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 343; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ASYMPTOTIC SOLUTIONS; BOUND STATE; DAMPING; ELECTRON PLASMA WAVES; INHOMOGENEOUS PLASMA; NONLINEAR PROBLEMS; POTENTIALS; SCHROEDINGER EQUATION; SOLITONS; TRANSFORMATIONS; WAVE PROPAGATION; WAVELENGTHS