Excitement of solitons in the interaction of kinks of sine-Gordon equation with attracting impurity [PDF]
Компьютерные исследования и моделирование, 2012 We investigate analytically and numerically the structure and properties of localized two- and three-kink solutions of the sine-Gordon equation, which are excited in the region of the attracting impurity.
Evgeniy Grigorevich Ekomasov +2 more
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Bidifferential Calculus, Matrix SIT and Sine-Gordon Equations
Acta Polytechnica, 2011 We express a matrix version of the self-induced transparency (SIT) equations in the bidifferential calculus framework. An infinite family of exact solutions is then obtained by application of a general result that generates exact solutions from solutions of a linear system of arbitrary matrix size.
Dimakis, A. +2 more
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Exploring Physics-Informed Neural Networks for the Generalized Nonlinear Sine-Gordon Equation
Applied Computational Intelligence and Soft ComputingThe nonlinear sine-Gordon equation is a prevalent feature in numerous scientific and engineering problems. In this paper, we propose a machine learning-based approach, physics-informed neural networks (PINNs), to investigate and explore the solution of ...
Alemayehu Tamirie Deresse +1 more
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Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems
, 2006 Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated.
Ariyasu +16 more
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Exact renormalization group and Sine Gordon theory
Journal of High Energy Physics, 2017 The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory.
Prafulla Oak, B. Sathiapalan
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AxiomsThis study explores the (1+1)-dimensional Klein–Fock–Gordon equation, a distinct third-order nonlinear differential equation of significant theoretical interest.
Muhammad Uzair +3 more
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Novel Exact Solutions of the Extended Shallow Water Wave and the Fokas Equations
ITM Web of Conferences, 2018 In this study, a Sine-Gordon expansion method for obtaining novel exact solutions of extended shallow water wave equation and Fokas equation is presented. All of the equations which are under consideration consist of three or four variable.
DURAN Serbay +2 more
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Geometrical interpretations of Bäcklund transformations and certain types of partial differential equations : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University [PDF]
, 2000 Page 37 is missing from the original copy.Gauss' Theorema Egregium contains a partial differential equation relating the Gaussian curvature K to components of the metric tensor and its derivatives.
Selvaratnam, Anton Raviraj
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AIP Advances, 2015 In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM) is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions.
H. S. Shukla +2 more
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PERTURBATION THEORY FOR SINE-GORDON EQUATION
Acta Physica Sinica, 1999 Making use of the method of multiple scales from the classical perturbation theory and the general method of Laplace transformation from the mathematical physics methods, we have solved the perturbation problem for sine-Gordon equation, and obtained the fist-order correction containing no secular terms, as well as the parameters slowly varied with time-
null TANG YI +3 more
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