(2+1)-dimensional local and nonlocal reductions of the negative AKNS system: Soliton solutions

Metin Gürses; Aslı Pekcan

doi:10.1016/j.cnsns.2018.11.016

(2+1)-dimensional local and nonlocal reductions of the negative AKNS system: Soliton solutions

Metin Gürses
, Aslı Pekcan

Division of Applied Mathematics

Bilkent University

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

We first construct a (2+1)-dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear forms of the negative AKNS hierarchy and give one- and two-soliton solutions. By using the soliton solutions of the negative AKNS hierarchy we find one-soliton solutions of the local and nonlocal reduced equations.

Original language	English
Pages (from-to)	161-173
Number of pages	13
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	71
DOIs	https://doi.org/10.1016/j.cnsns.2018.11.016
Publication status	Published - 15 Jun 2019

Keywords

(2+1)-dimensional negative AKNS hierarchy
Ablowitz–Musslimani reduction
Hirota bilinear method
Soliton solutions

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10.1016/j.cnsns.2018.11.016

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title = "(2+1)-dimensional local and nonlocal reductions of the negative AKNS system: Soliton solutions",

abstract = "We first construct a (2+1)-dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear forms of the negative AKNS hierarchy and give one- and two-soliton solutions. By using the soliton solutions of the negative AKNS hierarchy we find one-soliton solutions of the local and nonlocal reduced equations.",

keywords = "(2+1)-dimensional negative AKNS hierarchy, Ablowitz–Musslimani reduction, Hirota bilinear method, Soliton solutions",

author = "Metin G{\"u}rses and Aslı Pekcan",

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T1 - (2+1)-dimensional local and nonlocal reductions of the negative AKNS system

T2 - Soliton solutions

AU - Gürses, Metin

AU - Pekcan, Aslı

PY - 2019/6/15

Y1 - 2019/6/15

N2 - We first construct a (2+1)-dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear forms of the negative AKNS hierarchy and give one- and two-soliton solutions. By using the soliton solutions of the negative AKNS hierarchy we find one-soliton solutions of the local and nonlocal reduced equations.

AB - We first construct a (2+1)-dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear forms of the negative AKNS hierarchy and give one- and two-soliton solutions. By using the soliton solutions of the negative AKNS hierarchy we find one-soliton solutions of the local and nonlocal reduced equations.

KW - (2+1)-dimensional negative AKNS hierarchy

KW - Ablowitz–Musslimani reduction

KW - Hirota bilinear method

KW - Soliton solutions

UR - https://www.scopus.com/pages/publications/85057243473

U2 - 10.1016/j.cnsns.2018.11.016

DO - 10.1016/j.cnsns.2018.11.016

M3 - Article

AN - SCOPUS:85057243473

SN - 1007-5704

VL - 71

SP - 161

EP - 173

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

(2+1)-dimensional local and nonlocal reductions of the negative AKNS system: Soliton solutions

Abstract

Keywords

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