scholarly journals Nonlocal PT-Symmetric Integrable Equations of Fourth-Order Associated with so(3, ℝ)

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2130
Author(s):  
Li-Qin Zhang ◽  
Wen-Xiu Ma
Keyword(s):  
Conservation Laws ◽  
Lie Algebra ◽  
Integrable System ◽  
Fourth Order ◽  
Reverse Time ◽  
Integrable Equations

The paper aims to construct nonlocal PT-symmetric integrable equations of fourth-order, from nonlocal integrable reductions of a fourth-order integrable system associated with the Lie algebra so(3,R). The nonlocalities involved are reverse-space, reverse-time, and reverse-spacetime. All of the resulting nonlocal integrable equations possess infinitely many symmetries and conservation laws.

Riemann–Hilbert problems of a nonlocal reverse-time six-component AKNS system of fourth order and its exact soliton solutions

2021 ◽  
pp. 2150035
Author(s):  
Alle Adjiri ◽  
Ahmed M. G. Ahmed ◽  
Wen-Xiu Ma
Keyword(s):  
Fourth Order ◽  
Soliton Solutions ◽  
Reverse Time ◽  
Akns Hierarchy ◽  
Spectral Problems ◽  
Jump Matrix ◽  
Akns System ◽  
Associated Matrix ◽  
Time Reduction ◽  
Exact Soliton Solutions

We investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann–Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix.

scholarly journals A Fourth Order Entropy Stable Scheme for Hyperbolic Conservation Laws

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 508 ◽  
Author(s):  
Xiaohan Cheng
Keyword(s):  
Conservation Laws ◽  
Fourth Order ◽  
Hyperbolic Conservation Laws ◽  
Order Accuracy ◽  
Hyperbolic Conservation ◽  
Diffusion Operator ◽  
Sign Property ◽  
Entropy Stable ◽  
Order Four ◽  
Stable Scheme

This paper develops a fourth order entropy stable scheme to approximate the entropy solution of one-dimensional hyperbolic conservation laws. The scheme is constructed by employing a high order entropy conservative flux of order four in conjunction with a suitable numerical diffusion operator that based on a fourth order non-oscillatory reconstruction which satisfies the sign property. The constructed scheme possesses two features: (1) it achieves fourth order accuracy in the smooth area while keeping high resolution with sharp discontinuity transitions in the nonsmooth area; (2) it is entropy stable. Some typical numerical experiments are performed to illustrate the capability of the new entropy stable scheme.

Lie symmetries, conservation laws and analytical solutions for two-component integrable equations

2017 ◽  
Vol 55 (3) ◽  
pp. 996-1010 ◽  
Author(s):  
Lian-Li Feng ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang ◽  
Jun Zhou
Keyword(s):  
Conservation Laws ◽  
Analytical Solutions ◽  
Lie Symmetries ◽  
Integrable Equations ◽  
Two Component
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