Journal ArticleDOI
New periodic wave solutions of a time fractional integrable shallow water equation
TLDR
In this paper, the authors employed Jacobi elliptic function expansion method to build the new wave solutions of time fractional modified Camassa-Holm equation which is completely integrable dispersive shallow-water equation.About:
This article is published in Applied Ocean Research.The article was published on 2019-04-01. It has received 23 citations till now. The article focuses on the topics: Jacobi elliptic functions & Elliptic function.read more
Citations
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Nonlinear pulse propagation for novel optical solitons modeled by Fokas system in monomode optical fibers
TL;DR: In this paper , the Fokas system which represents the spread of irregular pulse in monomode optical fibers is investigated via the Jacobi elliptic function expansion (JEFE) method.
Journal ArticleDOI
New optical solitons of conformable resonant nonlinear Schrödinger's equation
TL;DR: In this paper, the Sardar sub-equation approach is applied to conformable resonant Schrödinger's equation, which is one of the strong methods for solving nonlinear evolution equations.
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New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method
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Specific wave structures of a fifth-order nonlinear water wave equation
K. Hosseini,Сергій Романенко,Mohammad Mirzazadeh,Louise Kerterz,Soheil Salahshour,Dumitru Baleanu,Dumitru Baleanu,Asim Zafar +7 more
TL;DR: In this paper, a traveling wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain, and the Kudryashov methods are then adopted as leading techniques to construct specific wave structures of the governing model which are classified as W -shaped and other solitons.
Journal ArticleDOI
Asymptotical stability analysis of conformable fractional systems
Yongfang Qi,Xuhuan Wang +1 more
TL;DR: In this article, the asymptotic stability of the system was analyzed in the form T α y ( τ ) = A y( τ ) + f ( τ, y(τ ) ) with the initial value y (τ 0 ) = y 0.
References
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Journal ArticleDOI
An integrable shallow water equation with peaked solitons
Roberto Camassa,Darryl D. Holm +1 more
TL;DR: A new completely integrable dispersive shallow water equation that is bi-Hamiltonian and thus possesses an infinite number of conservation laws in involution is derived.
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A new definition of fractional derivative
TL;DR: A new definition of fractional derivative and fractional integral is given and it is shown that it is the most natural definition, and the most fruitful one.
Journal ArticleDOI
On conformable fractional calculus
TL;DR: The basic concepts in this new simple interesting fractional calculus called conformable fractional derivative are set and the fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.
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Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
TL;DR: In this article, a Jacobi elliptic function expansion method was proposed to construct the exact periodic solutions of nonlinear wave equations, which includes some shock wave solutions and solitary wave solutions.
Journal ArticleDOI
The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations
Adrian Constantin,David Lannes +1 more
TL;DR: In this article, the authors prove that the nonlinear dispersive partial differential equations (NPDPDE) and Korteweg-de Vries (KDE) arise in the modeling of the propagation of shallow water waves over a flat bed.