Search Results - subject:"Sine-Gordon equation"

Dispersion, group velocity, and multisymplectic discretizations

Schober, C.M.; Wlodarczyk, T.H. - In: Mathematics and Computers in Simulation (MATCOM) 80 (2009) 4, pp. 741-751

This paper examines the dispersive properties of multisymplectic discretizations of linear and nonlinear PDEs. We focus on a leapfrog in space and time scheme and the Preissman box scheme. We find that the numerical dispersion relations are monotonic and determine the relationship between the...

Persistent link: https://www.econbiz.de/10010748727

A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

Dehghan, Mehdi; Shokri, Ali - In: Mathematics and Computers in Simulation (MATCOM) 79 (2008) 3, pp. 700-715

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a … numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using …

Persistent link: https://www.econbiz.de/10010749551

A third order numerical scheme for the two-dimensional sine-Gordon equation

Bratsos, A.G. - In: Mathematics and Computers in Simulation (MATCOM) 76 (2007) 4, pp. 271-282

A rational approximant of third order, which is applied to a three-time level recurrence relation, is used to transform the two-dimensional sine-Gordon (SG) equation into a second-order initial-value problem. The resulting nonlinear finite-difference scheme, which is analyzed for stability, is...

Persistent link: https://www.econbiz.de/10010748680

Negaton and complexiton solutions of sine-Gordon equation

Wu, Hongxia; Fan, Tianyou - In: Physica A: Statistical Mechanics and its Applications 379 (2007) 2, pp. 471-482

The negaton and complexiton solutions are introduced for the sine-Gordon equation by means of the Darboux … detail. The superposition formulae for negations and complexitons are constructed. Noticing the relation of the sine-Gordon … equation and the sinh-Gordon equation, we also obtain the real-valued singular negaton and complexiton solution for the sinh …

Persistent link: https://www.econbiz.de/10010590744

The variable separated ODE method for travelling wave solutions for the Boussinesq-double sine-Gordon and the Boussinesq-double sinh-Gordon equations

Wazwaz, Abdul-Majid - In: Mathematics and Computers in Simulation (MATCOM) 72 (2006) 1, pp. 1-9

Travelling wave solutions for the Boussinesq-double sine-Gordon (B-sine-Gordon) equation, the Boussinesq-double sinh …

Persistent link: https://www.econbiz.de/10010749013

Nonlinear fractional dynamics on a lattice with long range interactions

Laskin, N.; Zaslavsky, G. - In: Physica A: Statistical Mechanics and its Applications 368 (2006) 1, pp. 38-54

A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel–Kontorova chain model for the non-nearest interactions. Quantum...

Persistent link: https://www.econbiz.de/10011064584

Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme

Sheng, Q.; Khaliq, A.Q. M.; Voss, D.A. - In: Mathematics and Computers in Simulation (MATCOM) 68 (2005) 4, pp. 355-373

This paper proposes a split cosine scheme for simulating solitary solutions of the sine-Gordon equation in two …

Persistent link: https://www.econbiz.de/10010749626

Conformational transitions in polymers with nonlinear dissipative processes during electronic structure reconstruction

Shikhovtseva, E.S. - In: Physica A: Statistical Mechanics and its Applications 349 (2005) 3, pp. 421-430

Polymer conformational dynamics caused by soliton-like excitations propagation has been investigated. A full set of conformational transitions for quasi-one-dimensional bistable chains with complicated internal structure is presented. The influence of nonlinear friction during electronic...

Persistent link: https://www.econbiz.de/10010590454

The N-soliton solutions of the sine-Gordon equation with self-consistent sources

Zhang, Da-Jun; Chen, Deng-yuan - In: Physica A: Statistical Mechanics and its Applications 321 (2003) 3, pp. 467-481

The hierarchy of the sine-Gordon equation with self-consistent sources is derived by using the eigenfunctions of … recursion operator. The bilinear form of the sine-Gordon equation with self-consistent sources is given and the N …

Persistent link: https://www.econbiz.de/10010590026

Stability of phase transitions in polymers with bistable unit cells

Shikhovtseva, E.S. - In: Physica A: Statistical Mechanics and its Applications 303 (2002) 1, pp. 133-143

Soliton-like switching regimes are investigated for chains of bistable unit cells with energy non-degenerate ground states. It is shown that there is a set of equilibrium soliton velocities in the chains of bistable units with complicated internal structure. There are two essentially different...

Persistent link: https://www.econbiz.de/10010873929