A Numerical Study of the Light Bullets Interaction in the (2+1) Sine-Gordon Equation

Povich, Timothy James; Xin, Jack

doi:10.1007/s00332-003-0588-y

Cited by 9 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later, in Ref. [49], the robustness of the light bullets during collisions was shown. The 2D sG equation was written in the form which allows propagation in both directions (in contrast, what we got here is the one-directional form of the 2D sG equation), and the inputs were either counterpropagating or colliding at a large angle [49].…”

Section: Numerical Resolution Of 2d Sgmentioning

confidence: 97%

See 1 more Smart Citation

Ultrashort light bullets described by the two-dimensional sine-Gordon equation

Leblond

Mihalache

2010

Phys. Rev. A

View full text Add to dashboard Cite

By using a reductive perturbation technique applied to a two-level model, a generic twodimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly-varying envelope approximation is put forward. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal waveforms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time, and are therefore not steady-state lumps.

show abstract

Section: Numerical Resolution Of 2d Sgmentioning

confidence: 97%

“…[46], and even interactions have been studied in Ref. [49]. In [46], the 2D sG equation was also derived from the Maxwell-Bloch equations, but the derivation was performed from a reduced form of the Maxwell-Bloch equations, and the physical assumptions were not so cleary given.…”

Section: Numerical Resolution Of 2d Sgmentioning

confidence: 99%

Ultrashort light bullets described by the two-dimensional sine-Gordon equation

Leblond

Mihalache

2010

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…Sine-Gordon (SG) equation is a second-order hyperbolic partial differential equation whose numerical solutions depict the soliton form and have intense applications in science and engineering. It appears in the study of optics as a solution to the classical Maxwell systems [2]. This equation also appears in the literature in the geometrical study of the soliton in view of the canonical field [3].…”

Section: Introductionmentioning

confidence: 95%

Particle Swarm Optimization for Solving Sine-Gordan Equation

Arora¹,

Chauhan²,

Asjad³

et al. 2023

Computer Systems Science and Engineering

View full text Add to dashboard Cite

The term 'optimization' refers to the process of maximizing the beneficial attributes of a mathematical function or system while minimizing the unfavorable ones. The majority of real-world situations can be modelled as an optimization problem. The complex nature of models restricts traditional optimization techniques to obtain a global optimal solution and paves the path for global optimization methods. Particle Swarm Optimization is a potential global optimization technique that has been widely used to address problems in a variety of fields. The idea of this research is to use exponential basis functions and the particle swarm optimization technique to find a numerical solution for the Sine-Gordan equation, whose numerical solutions show the soliton form and has diverse applications. The implemented optimization technique is employed to determine the involved parameter in the basis functions, which was previously approximated as a random number in the work reported till now in the literature. The obtained results are comparable with the results obtained in the literature. The work is presented in the form of figures and tables and is found encouraging.

show abstract