Discrete rogue waves and blow-up from solitons of a nonisospectral semi-discrete nonlinear Schrödinger equation

Silem, Abdselam; Wu, Hua; Zhang, Da‐jun

doi:10.1016/j.aml.2021.107049

Cited by 24 publications

(6 citation statements)

References 21 publications

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“…Furthermore, the concept of discrete fractional calculus was rooted in the few decades; it gets attention of many researchers recently because of their inquisitive thinking (see [5][6][7] and references therein). The main reason is that these problems and operators have a wide range of practical applications, such as mathematical analysis [8,9], stability analysis [10][11][12], probability and statistics [13][14][15], geometry [16,17], ecology [18,19], and topology [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically

et al. 2023

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In this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann–Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the $\Delta ^{2}$ Δ 2 , which will be useful to obtain the convexity results. We examine the correlation between the positivity of $({}^{\mathrm{RL}}_{w_{0}}\Delta ^{\alpha} \mathrm{f} )( \mathrm{t})$ ( w 0 RL Δ α f ) ( t ) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of $(2,3)$ ( 2 , 3 ) , $\mathscr{H}_{\mathrm{k},\epsilon}$ H k , ϵ and $\mathscr{M}_{\mathrm{k},\epsilon}$ M k , ϵ . The decrease of these sets allows us to obtain the relationship between the negative lower bound of $({}^{\mathrm{RL}}_{w_{0}}\Delta ^{\alpha} \mathrm{f} )( \mathrm{t})$ ( w 0 RL Δ α f ) ( t ) and convexity of the function on a finite time set $\mathrm{N}_{w_{0}}^{\mathrm{P}}:=\{w_{0}, w_{0}+1, w_{0}+2,\dots , \mathrm{P}\}$ N w 0 P : = { w 0 , w 0 + 1 , w 0 + 2 , … , P } for some $\mathrm{P}\in \mathrm{N}_{w_{0}}:=\{w_{0}, w_{0}+1, w_{0}+2,\dots \}$ P ∈ N w 0 : = { w 0 , w 0 + 1 , w 0 + 2 , … } . The numerical part of the paper is dedicated to examinin the validity of the sets $\mathscr{H}_{\mathrm{k},\epsilon}$ H k , ϵ and $\mathscr{M}_{\mathrm{k},\epsilon}$ M k , ϵ for different values of k and ϵ. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.

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Section: Introductionmentioning

confidence: 99%

On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically

et al. 2023

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“…Since the discovery of the soliton Since the discovery of the soliton, experimental and theoretical approaches have been developed to search for novelty in specific physical systems. localized wave structures in specific physical systems, to investigate the mechanisms of generation of various localized waves, and to investigate the interactions between different localized waves Characteristics [9][10][11][12]. Since its exact solution is a special kind of solution and exists stably in space, it is of great practical importance for many complex physical phenomena and some nonlinear engineering problems.…”

Section: Introductionmentioning

confidence: 99%

Spatial Self-Bending Soliton Phenomenon of (2+1) Dimensional bidirectional Sawada-Kotera Equation

Wang¹

2023

Preprint

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In this paper, we mainly study the spatial self-bending soliton phenomenon of the (2+1) dimensional bidirection-al Sawada-Kotera equation. The bilinear form of the (2+1)-dimensional bidirectional Sawada-Kotera equation is obtained by Hirota bilinear method, and then the N-soliton solution is obtained through special parameter constraints (e A js = 0), the spatial self-bending soliton is derived from the N-soliton solution, and the curvature of the spatial self-bending soliton is given furthermore, the interaction solution of spatial self-bending soliton and respiratory wave is obtained, and the interaction solution of spatial self-bending soliton and higher-order lump wave is obtained by using the method of long wave limit.

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“…The important goal of these discrete operators is to convert the integral equations to system of sum equations, so their consideration provides more information regarding the nature of the development being modelled. Due to the association of DFC to practical ventures that are extensively employed to nanotechnology, optics, infectious diseases, physics, chaos theory, economics, medicine, among other areas, many researchers are devoting their attention to generalize the continuous problems to discrete fractional dynamics (see [1,[7][8][9]).…”

Section: Introductionmentioning

confidence: 99%

On Convexity, Monotonicity and Positivity Analysis for Discrete Fractional Operators Defined Using Exponential Kernels

et al. 2022

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This article deals with analysing the positivity, monotonicity and convexity of the discrete nabla fractional operators with exponential kernels from the sense of Riemann and Caputo operators. These operators are called discrete nabla Caputo–Fabrizio–Riemann and Caputo–Fabrizio–Caputo fractional operators. Further, some of our results concern sequential nabla Caputo–Fabrizio–Riemann and Caputo–Fabrizio–Caputo fractional differences, such as ∇aCFRμ∇bCFCυh(x), for various values of start points a and b, and for orders υ and μ in different ranges. Three illustrative examples of the main lemmas in the case of Riemann–Liouville are given at the end of the article.

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Discrete rogue waves and blow-up from solitons of a nonisospectral semi-discrete nonlinear Schrödinger equation

Cited by 24 publications

References 21 publications

On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically

On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically

Spatial Self-Bending Soliton Phenomenon of (2+1) Dimensional bidirectional Sawada-Kotera Equation

On Convexity, Monotonicity and Positivity Analysis for Discrete Fractional Operators Defined Using Exponential Kernels

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