Breather-type and multi-wave solutions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo linebreak="goodbreak">+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional nonlocal Gardner equation

Yaşar, Emrullah

doi:10.1016/j.amc.2020.125663

Cited by 9 publications

(2 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 1 represents the shock wave profile for Equation (26), and the transition of the wave is observed through the contour plots. Similarly, Figure 2 represents the shock wave for Equation (29). Figure 3 demonstrates the multisoliton wave profile for Equation (27).…”

Section: Discussionmentioning

confidence: 99%

“…The Gardner equation is applied on many scientific fields such as bottom topography [24], magnetoplasma [25], plasma physics [26], mechanical analysis [27], and lattice Boltzmann model [28]. Ozkan and Yasar [29] studied the exact solutions of the nonlocal Gardner equation by employing the Hirota bilinear, extended homoclinic, and three-wave methods to obtain solutions of breather-type and multi-wave-type solitons. Orhan and Ozer [30] studied the μ-symmetries, μ-reduction, and μ-conservation laws for the Gardner equation.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

See 1 more Smart Citation

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Mohanty

Dev

Sahoo³

et al. 2023

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized G ′ / G expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized G ′ / G expansion technique. The extended generalized G ′ / G expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of G ′ / G . The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Mohanty

Dev

Sahoo³

et al. 2023

Advances in Mathematical Physics

View full text Add to dashboard Cite

show abstract

Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model

et al. 2021

View full text Add to dashboard Cite

M-lump solutions, lump-breather solutions, and N-soliton wave solutions for the KP-BBM equation via the improved bilinear neural network method using innovative composite functions

Huang,

Zhu,

et al. 2024

Nonlinear Dyn

View full text Add to dashboard Cite

Breather-type and multi-wave solutions for(2+1)-dimensional nonlocal Gardner equation

Cited by 9 publications

References 39 publications

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model

M-lump solutions, lump-breather solutions, and N-soliton wave solutions for the KP-BBM equation via the improved bilinear neural network method using innovative composite functions

Contact Info

Product

Resources

About

Breather-type and multi-wave solutions for(2+1)-dimensional nonlocal Gardner equation

Cited by 9 publications

References 39 publications

Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model

M-lump solutions, lump-breather solutions, and N-soliton wave solutions for the KP-BBM equation via the improved bilinear neural network method using innovative composite functions

Contact Info

Product

Resources

About

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method