On novel nondifferentiable exact solutions to local fractional Gardner's equation using an effective technique
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7060
Abstract: One of the most interesting branches of fractional calculus is the local fractional calculus, which has been used successfully to describe many fractal problems in science and engineering. The main purpose of this contribution is… read more here.
Keywords: local fractional; fractional gardner; gardner equation; solutions local ... See more keywords
The Role of a Thick Soliton in the Dynamics of the Soliton Gas Within the Framework of the Gardner Equation
Sign Up to like & getrecommendations! Published in 2019 at "Radiophysics and Quantum Electronics"
DOI: 10.1007/s11141-019-09922-9
Abstract: We study the statistical moments of the soliton gas (mean field, variance, skewness, and kurtosis), which is described within the framework of the Gardner equation with negative cubic nonlinearity. The influence of the limiting (thick… read more here.
Keywords: framework gardner; soliton; within framework; soliton gas ... See more keywords
A group theoretic analysis of the generalised Gardner equation with arbitrary order nonlinear terms
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.07.036
Abstract: Abstract In this paper, we analyse a Gardner equation with dual power law nonlinearity of any order which has been widely investigated due to its applications in quantum field theory, solid state, plasma and fluid… read more here.
Keywords: order; group theoretic; equation; analysis ... See more keywords
Simulation study on nonlinear structures in nonlinear dispersive media.
Sign Up to like & getrecommendations! Published in 2020 at "Chaos"
DOI: 10.1063/1.5132557
Abstract: In this work, the dynamic mechanism scenario of nonlinear electrostatic structures (unmodulated and modulated waves) that can propagate in multi-ion plasmas with the mixture of sulfur hexafluoride and argon gas is reported. For this purpose,… read more here.
Keywords: gardner equation; nonplanar gardner; study; simulation ... See more keywords
Exponential B-spline collocation solutions to the Gardner equation
Sign Up to like & getrecommendations! Published in 2020 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2019.1594791
Abstract: ABSTRACT Exponential B-splines are used to set up a collocation method for solving the Gardner equation. The space reduction of the Gardner equation is carried out to be able to obtain an exponential B-spline approximation… read more here.
Keywords: gardner equation; collocation; spline collocation; exponential spline ... See more keywords
Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation
Sign Up to like & getrecommendations! Published in 2022 at "The Scientific World Journal"
DOI: 10.1155/2022/3240918
Abstract: In this paper, some exact traveling wave solutions to the integrable Gardner equation are reported. The ansatz method is devoted for deriving some exact solutions in terms of Jacobi and Weierstrass elliptic functions. The obtained… read more here.
Keywords: equation; forced damped; numeric solutions; damped gardner ... See more keywords
Simulation of generalized time fractional Gardner equation utilizing in plasma physics for non-linear propagation of ion-acoustic waves
Sign Up to like & getrecommendations! Published in 2023 at "Thermal Science"
DOI: 10.2298/tsci23s1121i
Abstract: In this work, radial basis function collocation method (RBFCM) is implemented for generalized time fractional Gardner equation (GTFGE). The RBFCM is meshless and easy-to-implement in complex geometries and higher dimensions, therefore, it is highly demanding.… read more here.
Keywords: time; time fractional; physics; generalized time ... See more keywords
Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients
Sign Up to like & getrecommendations! Published in 2021 at "Symmetry"
DOI: 10.3390/sym13122434
Abstract: In this paper, we employ the certain theory of Lie symmetry analysis to discuss the time-fractional Gardner equation with time-dependent coefficients. The Lie point symmetry is applied to realize the symmetry reduction of the equation,… read more here.
Keywords: time; fractional gardner; gardner equation; conservation ... See more keywords
Atomic Solution for Certain Gardner Equation
Sign Up to like & getrecommendations! Published in 2023 at "Symmetry"
DOI: 10.3390/sym15020440
Abstract: In this paper, a new technique using a tensor product is presented in order to provide exact solutions to some certain fractional differential equations. Particularly, the well-known third order Gardner’s equation, which is also known… read more here.
Keywords: solution certain; gardner equation; atomic solution;