Nonlocal Short Pulse Equations

Nonlocal Short Pulse Equations We introduce nonlocal integrable reductions of the Wadati-Konno-Ichikawa (WKI) coupled equations. Using the nonlocal reductions of Ablowitz and Musslimani, we obtain new integrable equations such as the nonlocal short pulse (SP) equations and the nonlocal elastic beam (EB) equations. Keywords Short pulse equation · Integrable models · Nonlocal nonlinear evolution equations Integro-differential nonlocal integrable equations such as The matrix B for the evolution of the eigenfunctions ψ , ψ 1 2 the Benjamin-Ono equation [1–3], intermediate long wave is given by ⎛ ⎞ equation [4, 5], Hunter-Saxon equation [6, 7], isentropic AB gas dynamics equation [8], short pulse (SP) equation ⎝ ⎠ B = , [9, 10], Ostrovsky-Vakhnenko equation [11] among many C −A others are very common in the study of integrable models. where A, B,and C are scalar functions of q(x, t), r(x, t) Contrasting with these equations, Ablowitz and Musslimani and λ. The compatibility condition of the system (1), i.e., [12] have introduced a new class of nonlocal equations =  , yields the so called zero curvature (ZC) xt tx from nonlocal reductions of certain integrable coupled representation differential equations. The starting point is the Ablowitz- Kaup-Newell-Segur (AKNS) scattering problem [13, 14] A − B http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Brazilian Journal of Physics Springer Journals

Nonlocal Short Pulse Equations

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Publisher
Springer US
Copyright
Copyright © 2018 by Sociedade Brasileira de Física
Subject
Physics; Physics, general
ISSN
0103-9733
eISSN
1678-4448
D.O.I.
10.1007/s13538-018-0580-x
Publisher site
See Article on Publisher Site

Abstract

We introduce nonlocal integrable reductions of the Wadati-Konno-Ichikawa (WKI) coupled equations. Using the nonlocal reductions of Ablowitz and Musslimani, we obtain new integrable equations such as the nonlocal short pulse (SP) equations and the nonlocal elastic beam (EB) equations. Keywords Short pulse equation · Integrable models · Nonlocal nonlinear evolution equations Integro-differential nonlocal integrable equations such as The matrix B for the evolution of the eigenfunctions ψ , ψ 1 2 the Benjamin-Ono equation [1–3], intermediate long wave is given by ⎛ ⎞ equation [4, 5], Hunter-Saxon equation [6, 7], isentropic AB gas dynamics equation [8], short pulse (SP) equation ⎝ ⎠ B = , [9, 10], Ostrovsky-Vakhnenko equation [11] among many C −A others are very common in the study of integrable models. where A, B,and C are scalar functions of q(x, t), r(x, t) Contrasting with these equations, Ablowitz and Musslimani and λ. The compatibility condition of the system (1), i.e., [12] have introduced a new class of nonlocal equations =  , yields the so called zero curvature (ZC) xt tx from nonlocal reductions of certain integrable coupled representation differential equations. The starting point is the Ablowitz- Kaup-Newell-Segur (AKNS) scattering problem [13, 14] A − B

Journal

Brazilian Journal of PhysicsSpringer Journals

Published: May 30, 2018

References

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