scholarly journals A New Evans Function for Quasi-Periodic Solutions of the Linearised Sine-Gordon Equation

2020 ◽  
Vol 30 (6) ◽  
pp. 3421-3442 ◽  
Author(s):  
W. A. Clarke ◽  
R. Marangell
Keyword(s):  
Periodic Solutions ◽  
Gordon Equation ◽  
Evans Function ◽  
Sine Gordon Equation

Quasi-periodic solutions of the sine-Gordon equation

1982 ◽  
Vol 92 (9) ◽  
pp. 427-430 ◽  
Author(s):  
M. Jaworski ◽  
J. Zagrodziński
Keyword(s):  
Periodic Solutions ◽  
Gordon Equation ◽  
Sine Gordon Equation

scholarly journals Exact Traveling Wave Solutions for the Modified Double Sine-Gordon Equation

2015 ◽  
Vol 7 (2) ◽  
pp. 182
Author(s):  
Ying Huang ◽  
Bao Rong Li
Keyword(s):  
Periodic Solutions ◽  
Traveling Wave ◽  
Gordon Equation ◽  
Traveling Wave Solutions ◽  
Sine Gordon Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Different Types ◽  
Elementary Methods ◽  
Sg Equation

With some elementary  methods, a number of new travelling  solutions of  the  modified double Sine-Gordon (SG) equation are obtained,including different types of exact solion solutions and exact periodic solutions.

Numerical simulation of quasi-periodic solutions of the sine-Gordon equation

1995 ◽  
Vol 87 (1-4) ◽  
pp. 37-47 ◽  
Author(s):  
Mark J. Ablowitz ◽  
B.M. Herbst ◽  
Constance M. Schober
Keyword(s):  
Numerical Simulation ◽  
Periodic Solutions ◽  
Gordon Equation ◽  
Sine Gordon Equation

scholarly journals Duality of positive and negative integrable hierarchies via relativistically invariant fields

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
S. Y. Lou ◽  
X. B. Hu ◽  
Q. P. Liu
Keyword(s):  
Integrable Hierarchies ◽  
Gordon Equation ◽  
Formal Series ◽  
Two Dimensional ◽  
Relativistic Invariance ◽  
Sine Gordon Equation ◽  
Recursion Operators ◽  
Symmetry Approach ◽  
Duality Relations ◽  
Duality Problem

Abstract It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual relations, some continuous and discrete integrable positive hierarchies such as the potential modified Korteweg-de Vries hierarchy, the potential Fordy-Gibbons hierarchies, the potential dispersionless Kadomtsev-Petviashvili-like (dKPL) hierarchy, the differential-difference dKPL hierarchy and the second heavenly hierarchies are converted to the integrable negative hierarchies including the sG hierarchy and the Tzitzeica hierarchy, the two-dimensional dispersionless Toda hierarchy, the two-dimensional Toda hierarchies and negative heavenly hierarchy. In (1+1)-dimensional cases the positive/negative hierarchy dualities are guaranteed by the dualities between the recursion operators and their inverses. In (2+1)-dimensional cases, the positive/negative hierarchy dualities are explicitly shown by using the formal series symmetry approach, the mastersymmetry method and the relativistic invariance of the duality relations. For the 4-dimensional heavenly system, the duality problem is studied firstly by formal series symmetry approach. Two elegant commuting recursion operators of the heavenly equation appear naturally from the formal series symmetry approach so that the duality problem can also be studied by means of the recursion operators.

Sign in / Sign up

Export Citation Format

Share Document