Dynamics of ac-driven sine-Gordon equation for long Josephson junctions with fast varying perturbation

Gul, Zamin; Ali, Amir; Ahmad, I.

doi:10.1016/j.chaos.2017.12.025

Cited by 7 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By considering u≃ sin u, the considered system becomes the Sine-Gordon equation. In future work, it will be interesting to investigate the Sine-Gordon model with nonlinear AC/DC drives with different fractional operators to study the solitonic behavior, localized modes in single and in stacked long Josephson junctions with a variety of potentials, parity time symmetry, the nonlinearity/dispersion effects, and evolution of the localized monotonic shocks [67][68][69][70][71][72][73].…”

Section: Discussionmentioning

confidence: 99%

Time-Fractional Klein–Gordon Equation with Solitary/Shock Waves Solutions

Saifullah

Ali

Irfan

et al. 2021

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

In this article, we study the time-fractional nonlinear Klein–Gordon equation in Caputo–Fabrizio’s sense and Atangana–Baleanu–Caputo’s sense. The modified double Laplace transform decomposition method is used to attain solutions in the form of series of the proposed model under aforesaid fractional operators. The suggested method is the composition of the double Laplace transform and decomposition method. The convergence of the considered method is demonstrated for the considered model. It is observed that the obtained solutions converge to the exact solution of the proposed model. For validity, we consider two particular examples with appropriate initial conditions and derived the series solution in the sense of both operators for the considered model. From numerical solutions, it is observed that the considered model admits pulse-shaped solitons. It is also observed that the wave amplitude enhances with variations in time, which infers the coefficient α significantly increases the wave amplitude and affects the nonlinearity/dispersion effects, therefore may admit monotonic shocks. The physical behavior of the considered numerical examples is illustrated explicitly which reveals the evolution of localized shock excitations.

show abstract

Section: Discussionmentioning

confidence: 99%

Time-Fractional Klein–Gordon Equation with Solitary/Shock Waves Solutions

Saifullah

Ali

Irfan

et al. 2021

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

Localized modes in a variety of driven long Josephson junctions with phase shifts

Gul

Ali

2018

Nonlinear Dyn

View full text Add to dashboard Cite

New exact solutions of the (3+1)-dimensional double sine-Gordon equation by two analytical methods

Manzoor,

Iqbal,

Ashraf

et al. 2024

Opt Quant Electron

View full text Add to dashboard Cite

The (3+1)-dimensional double sine-Gordon equation plays a crucial role in various physical phenomena, including nonlinear wave propagation, field theory, and condensed matter physics. However, obtaining exact solutions to this equation faces significant challenges. In this article, we successfully employ a modified $$ \left( \dfrac{G'}{G^2}\right) $$ G ′ G 2 -expansion and improved $$\tan \left( \dfrac{\phi \left( \xi \right) }{2}\right) $$ tan ϕ ξ 2 -expansion methods to construct new analytical solutions to the double sine-Gordon equation. These solutions can be divided into four categories like trigonometric function solutions, hyperbolic function solutions, exponential solutions, and rational solutions. Our key findings include a rich spectrum of soliton solutions, encompassing bright, dark, singular, periodic, and mixed types, showcasing the (3+1)-dimensional double sine-Gordon equation ability to model diverse wave behaviors. We uncover previously unreported complex wave structures, revealing the potential for complex nonlinear interactions within the (3+1)-dimensional double sine-Gordon equation framework. We demonstrate the modified $$ \left( \dfrac{G'}{G^2}\right) $$ G ′ G 2 -expansion and improved $$\tan \left( \dfrac{\phi \left( \xi \right) }{2}\right) $$ tan ϕ ξ 2 -expansion methods effectiveness in handling higher-dimensional nonlinear partial differential equations, expanding their applicability in mathematical physics. These method offers enhanced flexibility and broader solution categories compared to conventional approaches.

show abstract

Dynamics of ac-driven sine-Gordon equation for long Josephson junctions with fast varying perturbation

Cited by 7 publications

References 16 publications

Time-Fractional Klein–Gordon Equation with Solitary/Shock Waves Solutions

Time-Fractional Klein–Gordon Equation with Solitary/Shock Waves Solutions

Localized modes in a variety of driven long Josephson junctions with phase shifts

New exact solutions of the (3+1)-dimensional double sine-Gordon equation by two analytical methods

Contact Info

Product

Resources

About