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

2018 ◽  
Vol 37 (5) ◽  
pp. 6359-6375 ◽  
Author(s):  
Wen-Xiu Ma
Keyword(s):  
Fourth Order ◽  
Soliton Solutions ◽  
Akns System

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 Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Bright Soliton ◽  
New Wave ◽  
Wave Patterns

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.

New (3+1)-dimensional integrable fourth-order nonlinear equation: lumps and multiple soliton solutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Fourth Order ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Lump Solutions ◽  
Content Type ◽  
Multiple Soliton Solutions ◽  
Order Nonlinear Equation ◽  
New Equation ◽  
Practical Implications

Purpose This paper aims to introduce a new (3 + 1)-dimensional fourth-order integrable equation characterized by second-order derivative in time t. The new equation models both right- and left-going waves in a like manner to the Boussinesq equation. Design/methodology/approach This formally uses the simplified Hirota’s method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space. Findings This paper confirms the complete integrability of the newly developed (3 + 1)-dimensional model in the Painevé sense. Research limitations/implications This paper addresses the integrability features of this model via using the Painlevé analysis. Practical implications This paper presents a variety of lump solutions via using a variety of numerical values of the included parameters. Social implications This work formally furnishes useful algorithms for extending integrable equations and for the determination of lump solutions. Originality/value To the best of the author’s knowledge, this paper introduces an original work with newly developed integrable equation and shows useful findings of solitons and lump solutions.

THE NAMBU-JONA-LASINIO SOLITON WITH GENERALIZED SCALAR INTERACTIONS

1993 ◽  
Vol 08 (01) ◽  
pp. 79-88 ◽  
Author(s):  
C. WEISS ◽  
R. ALKOFER ◽  
H. WEIGEL
Keyword(s):  
Fourth Order ◽  
Scalar Meson ◽  
Order Term ◽  
Soliton Solutions ◽  
Meson Field ◽  
Scale Invariant ◽  
Scalar Glueball ◽  
Fourth Order Term ◽  
Scalar Meson Field

Soliton solutions are studied as a generalization of the bosonized Nambu-Jona-Lasinio model with a fourth order term in the scalar meson field. Such an interaction arises in the context of a scale-invariant modification of the Nambu-Jona-Lasinio action, in which the scalar meson field is coupled to a scalar glueball field. It is shown that a fourth order term in the scalar meson field is crucial for the existence of stable solitons. We investigate the dependence of soliton properties on the scalar-glueball coupling.

scholarly journals HOPF SOLITON SOLUTIONS FROM LOW ENERGY EFFECTIVE ACTION OF SU(2) YANG–MILLS THEORY

2006 ◽  
Vol 21 (15) ◽  
pp. 1189-1202 ◽  
Author(s):  
NOBUYUKI SAWADO ◽  
NORIKO SHIIKI ◽  
SHINGO TANAKA
Keyword(s):  
Fourth Order ◽  
Effective Action ◽  
Dimensional Space ◽  
Soliton Solutions ◽  
Low Energy ◽  
Effective Theory ◽  
Second Derivative ◽  
Yang Mills ◽  
Extended Action ◽  
Derivative Term

The Skyrme–Faddeev–Niemi (SFN) model which is an O(3) σ-model in three-dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang–Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang–Mills theory recovers the SFN in the infrared region. However, the theory contains another fourth-order term which destabilizes soliton solutions. We find the stable soliton solutions in this extended action, introducing a second derivative term as a stabilizer. A perturbative technique for the second derivative term is applied to exclude (or reduce) the ill behavior of the action. A new topological energy bound formula is inferred for the action.

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