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Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy
Author(s) -
Chen Kui,
Deng Xiao,
Lou Senyue,
Zhang Dajun
Publication year - 2018
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12215
Subject(s) - wronskian , hierarchy , mathematics , soliton , nonlinear system , sine gordon equation , variation of parameters , mathematical physics , mathematical analysis , physics , differential equation , quantum mechanics , economics , market economy
In this paper, nonlocal reductions of the Ablowitz–Kaup–Newell–Suger (AKNS) hierarchy are collected, including the nonlocal nonlinear Schrödinger hierarchy, nonlocal modified Korteweg‐de Vries hierarchy, and nonlocal versions of the sine‐Gordon equation in nonpotential form. A reduction technique for solutions is employed, by which exact solutions in double Wronskian form are obtained for these reduced equations from those double Wronskian solutions of the AKNS hierarchy. As examples of dynamics, we illustrate new interaction of two‐soliton solutions of the reverse‐ t nonlinear Schrödinger equation. Although as a single soliton, it is stationary that two solitons travel along completely symmetric trajectories in { x , t } plane and their amplitudes are affected by phase parameters. Asymptotic analysis is given as demonstration. The approach and relation described in this paper are systematic and general and can be used to other nonlocal equations.