A REMARK ON SPIN AND STATISTICS OF BABY SKYRMION

1991 ◽  
Vol 06 (30) ◽  
pp. 2775-2783 ◽  
Author(s):  
HIDEHARU OTSU ◽  
TOSHIRO SATO
Keyword(s):  
Soliton Solution ◽  
Topological Charge ◽  
Topological Soliton ◽  
Spin And Statistics

We study spin and statistics of baby skyrmion, which is a topological soliton solution in the (2+1)-dimensional O(3) σ-model. It is shown that the Hopf term written in terms of CP 1 variables does not naively represent the topological charge associated with the non-triviality of Π1 (S2 → S2). It is also pointed out, therefore, that the baby skyrmion cannot behave as anyon, even if the Hopf term of CP 1 variables is added to the model.

scholarly journals Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in(1+1)-Dimensions with Power Law Nonlinearity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ming Song ◽  
Bouthina S. Ahmed ◽  
Anjan Biswas
Keyword(s):  
Finite Difference ◽  
Numerical Simulations ◽  
Power Law ◽  
Soliton Solution ◽  
Bifurcation Analysis ◽  
Soliton Solutions ◽  
Phase Portraits ◽  
Zakharov Equation ◽  
Topological Soliton ◽  
Klein Gordon

This paper addresses the Klein-Gordon-Zakharov equation with power law nonlinearity in (1+1)-dimensions. The integrability aspect as well as the bifurcation analysis is studied in this paper. The numerical simulations are also given where the finite difference approach was utilized. There are a few constraint conditions that naturally evolve during the course of derivation of the soliton solutions. These constraint conditions must remain valid in order for the soliton solution to exist. For the bifurcation analysis, the phase portraits are also given.

OPTICAL SOLITON SOLUTIONS OF THE LONG-SHORT-WAVE INTERACTION SYSTEM

2013 ◽  
Vol 22 (02) ◽  
pp. 1350015 ◽  
Author(s):  
AHMET BEKIR ◽  
ESIN AKSOY ◽  
ÖZKAN GÜNER
Keyword(s):  
Soliton Solution ◽  
Function Method ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Short Wave ◽  
Optical Soliton ◽  
Physical Parameters ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Dependent Model

This paper, studies the long-short-wave interaction (LS) equation. An optical soliton solution is obtained by the exp-function method and the ansatz method. Subsequently, we formally derive the dark (topological) soliton solutions for this equation. By using the exp-function method, some additional solutions will be derived. The physical parameters in the soliton solutions of ansatz method: amplitude, inverse width, and velocity are obtained as functions of the dependent model coefficients.

scholarly journals Exact solutions of the 2+1-dimensional Camassa–Holm Kadomtsev–Petviashvili equation

2012 ◽  
Vol 17 (3) ◽  
pp. 280-296 ◽  
Author(s):  
Ghodrat Ebadi ◽  
Nazila Yousefzadeh Fard ◽  
Houria Triki ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Exponential Function ◽  
Soliton Solution ◽  
Function Method ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Petviashvili Equation ◽  
Exponential Function Method

This paper studies the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation. There are a few methods that will be utilized to carry out the integration of this equation. Those are the G'/G method as well as the exponential function method. Subsequently, the ansatz method will be applied to obtain the topological soliton solution of this equation. The constraint conditions, for the existence of solitons, will also fall out of these.

Integrable Models

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Fluid Mechanics ◽  
Soliton Solution ◽  
Water Waves ◽  
Heisenberg Model ◽  
Kdv Equation ◽  
Short Review ◽  
Lax Pair ◽  
Shallow Water Waves ◽  
Initial Value ◽  
The Kdv Equation

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a channel. The exact soliton solution of this equation is derived. The Lax pair formalism for solving the general initial value problem is outlined. Two hamiltonian formalisms for the KdV equation (Fadeev–Zakharov and Magri) are explained. Then a short review of the geometry of curves (Frenet–Serret equations) is given. They are used to derive a remarkably simple equation for the propagation of a kink along a vortex filament. This equation of Hasimoto has surprising connections to the nonlinear Schrödinger equation and to the Heisenberg model of ferromagnetism. An exact soliton solution is found.

Dark soliton solution of Sasa-Satsuma equation

2010 ◽  
Author(s):  
Y. Ohta ◽  
Wen Xiu Ma ◽  
Xing-biao Hu ◽  
Qingping Liu
Keyword(s):  
Soliton Solution ◽  
Dark Soliton
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