Relevant bibliographies by topics / Sine-Gordon Type System

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Academic literature on the topic 'Sine-Gordon Type System'

Author: Grafiati
Published: 4 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Sine-Gordon Type System"

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S., Manna M. Sabawi and Y. Sabawi. "A Numerical Solution for Sine-Gordon Type System." System, Tikrit Journal of Pure Science 15, no. 3 (2010): 106–13. https://doi.org/10.5281/zenodo.3370232.

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Abstract  A numerical solution for Sine-Gordon type system was done by the use of two finite difference schemes, the first is the explicit scheme and the second is the Crank-Nicholson scheme. A comparison between the two schemes showed that the explicit scheme is easier and has faster convergence than the Crank-Nicholson scheme which is more accurate. The MATLAB environment  was used for the numerical computations.
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Khasanov, A. B., Kh N. Normurodov, and T. G. Khasanov. "Integration of a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions." Ukrains’kyi Matematychnyi Zhurnal 76, no. 8 (2024): 1217–34. http://dx.doi.org/10.3842/umzh.v76i8.7610.

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UDC 517.9 The method of inverse spectral problem is used to integrate a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions. The evolution of the spectral data for the periodic Dirac operator is introduced in which the coefficient of the Dirac operator is a solution of a nonlinear sine-Gordon–Liouville-type equation. The solvability of the Cauchy problemc is proved for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions. It is shown that the sum of a uniformly con
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Yildirim, Ozgur. "Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems." e-Journal of Analysis and Applied Mathematics 2024 (December 31, 2024): 47–70. https://doi.org/10.62780/ejaam/2024-005.

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This paper presents the existence and uniqueness of the weak solution for the nonlinear system of sine-Gordon equations which describes DNA dynamics. An unconditionally stable second order difference scheme generated by the unbounded operator A2 corresponding to the system of sine-Gordon equations is considered. Weak solutions are a more general type of solution to the system of sine-Gordon equations than classical solutions and are important in the case of low regularity conditions. The weak solvability is studied in the space of distributions using variational methods. A very efficient numer
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Khasanov, A. B., and Kh N. Normurodov. "Integration of a sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 3 (April 9, 2024): 70–83. http://dx.doi.org/10.26907/0021-3446-2024-3-70-83.

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In this paper, the inverse spectral problem method is used to integrate a nonlinear sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly convergent functional series constructed by solving the system of Dubrovin equations and the first trace formula satisfies sine-Gordon-type equations with an additional term.
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REINISCH, G. "NONLINEAR KLEIN-GORDON SOLITON MECHANICS." International Journal of Modern Physics B 06, no. 21 (1992): 3395–440. http://dx.doi.org/10.1142/s021797929200150x.

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Nonlinear Klein-Gordon solitary waves — or “solitons” in a loose sense — in n+1 dimensions, driven by very general external fields which must only satisfy continuity — together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom — which may be conservative or not — of the second Newton’s law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force
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Ivanov, B. A., and E. V. Tartakovskaya. "Phonon relaxation of kink-type solitons in quasi-one-dimensional ordered systems." Soviet Journal of Low Temperature Physics 12, no. 10 (1986): 613–18. https://doi.org/10.1063/10.0031592.

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The interaction of the order parameter of a one-dimensional nonlinear system with elastic excitations of a three-dimensional matrix is investigated. The kinetic coefficients of the “kink gas” are calculated in the flexible-chain and rigid-chain approximations for two models of the nonlinear system (sine–Gordon and Φ(4)). The contribution of phonon processes in the relaxation of the system to an equilibrium state is analyzed, and the temperature dependence of the kinetic coefficients of the kink gas is determined.
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Rout, Abhishek, and Brett Altschul. "Bound States and Particle Production by Breather-Type Background Field Configurations." Symmetry 16, no. 12 (2024): 1571. http://dx.doi.org/10.3390/sym16121571.

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We investigate the interaction of fermion fields with oscillating domain walls, inspired by breather-type solutions of the sine-Gordon equation, a nonlinear system of fundamental importance. Our study focuses on the fermionic bound states and particle production induced by a time-dependent scalar background field. The fermions couple to two domain walls undergoing harmonic motion, and we explore the resulting dynamics of the fermionic wave functions. We demonstrate that while fermions initially form bound states around the domain walls, the energy provided by the oscillatory motion of the scal
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Ma, Hong-Cai, and Sen Yue Lou. "Solutions Generated from the Symmetry Group of the (2 + 1)-Dimensional Sine-Gordon System." Zeitschrift für Naturforschung A 60, no. 4 (2005): 229–36. http://dx.doi.org/10.1515/zna-2005-0403.

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Jha, Navnit, Venu Gopal, and Bhagat Singh. "Geometric grid network and third-order compact scheme for solving nonlinear variable coefficients 3D elliptic PDEs." International Journal of Modeling, Simulation, and Scientific Computing 09, no. 06 (2018): 1850053. http://dx.doi.org/10.1142/s1793962318500538.

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By using nonuniform (geometric) grid network, a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type. Single cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical solutions. The monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution values. As an experiment, applications of the compact scheme to Schrödinger equations, sine-Gordo
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Selvaratnam, A. R., M. Vlieg-Hulstman, B. van-Brunt, and W. D. Halford. "On the solution of a class of second-order quasi-linear PDEs and the Gauss equation." ANZIAM Journal 42, no. 3 (2001): 312–23. http://dx.doi.org/10.1017/s1446181100011962.

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AbstractGauss' Theorema Egregium produces a partial differential equation which relates the Gaussian curvature K to components of the metric tensor and its derivatives. Well-known partial differential equations (PDEs) such as the Schrödinger equation and the sine-Gordon equation can be derived from Gauss' equation for specific choices of K and coördinate systems. In this paper we consider a class of Bäcklund Transformations which corresponds to coördinate transformations on surfaces with a given Gaussian curvature. These Bäcklund Transformations lead to the construction of solutions to certain
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Book chapters on the topic "Sine-Gordon Type System"

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Carretero-González, R., D. J. Frantzeskakis, and P. G. Kevrekidis. "Interlude: Numerical Considerations for Nonlinear Wave Equations." In Nonlinear Waves & Hamiltonian Systems. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/oso/9780192843234.003.0017.

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Abstract This chapter presents some basic numerical techniques based on finite difference discretizations to find steady states of PDEs and their corresponding stability spectra. The (spatial) discretization allows us to cast an approximation to the original PDE as a system of coupled ODEs, namely a dynamical lattice. Importantly, this allows us to write algebraic (nonlinear) equations for steady states that can be solved using Newton-type methods. In turn, the stability of these steady states can be determined by computing the corresponding stability eigenvalue spectrum. Finally, we describe
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