Looking at a nonlinear inhomogeneous optical fiber through the generalized higher-order variable-coefficient Hirota equation

Gao, Xin-Yi

doi:10.1016/j.aml.2017.03.020

Cited by 163 publications

(20 citation statements)

References 38 publications

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“…for some functions T i [u]. If u = u (X) is a solution for Equation 16, then Equation 18 gives the Cls 36…”

Section: The Multipliers Of Equation 16 Are a Function {ξ [U]} Such Thatmentioning

confidence: 99%

“…On the other hand, when the inhomogeneities of media are taken into account, that is the NLEE are considered with space variable coefficients. This case represents more realistic models than those which are considered with constant coefficients . The soliton wave propagation in the above‐mode has been called “non‐autonomous soliton.” Hence, N‐soliton nonautonomous soliton interactions in various play a definitive role in the formation of the structure of wave and also the propagation direction with a phase shift in dispersive media …”

Section: Introductionmentioning

confidence: 99%

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On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Abdel‐Gawad

Tantawy

Yusuf

2019

Math Methods in App Sciences

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In this article, the generalized unified method (GUM) is used for finding multiwave solutions of the coupled Whitham‐Broer‐Kaup (WBK) equation with variable coefficients. Which describes the propagation of of shallow water waves. Here, we study the effects of the indirect nonlinear interaction of one‐, two‐ and three‐solitonic similaritons on the behavior of propagation of waves, in quasi‐periodic distributed system. This study can unable us to control the dynamics of type soliton (soliton, anti‐soliton) similaritons waves in dispersive waveguides. To give more physical insight to the obtained solutions, they are shown graphically. Their different structures are depicted by taking appropriate arbitrary functions. Further, with the suitable parameters, the indirect nonlinear interaction between two and three‐soliton waves are shown weal, in the sense that their amplitude does not blow up. Moreover, because of the importance of conservation laws Cls and stability analysis SA in the investigation of integrability, internal properties, existence, and uniqueness of a differential equation, we compute the Cls via multiplier technique and stability analysis via the concept of linear stability analysis for the WBK equations using the constant coefficients.

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“…for some functions T i [u]. If u = u (X) is a solution for Equation 16, then Equation 18 gives the Cls 36…”

Section: The Multipliers Of Equation 16 Are a Function {ξ [U]} Such Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Abdel‐Gawad

Tantawy

Yusuf

2019

Math Methods in App Sciences

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“…In general, the nonlinear partial di erential equations (NPDEs) have modeled nonlinear complex phenomena in various scienti c elds [24][25][26][27][28][29][30][31][32][33][34][35]. e investigation of analytical, approximate, and exact solutions of NPDEs will help better understand the complex phynomena.…”

Section: Introductionmentioning

confidence: 99%

On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations

Eladdad

Tarif

2019

Advances in Mathematical Physics

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“…Many methods are used to obtain the soliton solutions for nonlinear evolution equations (NLEEs), such as G ′ / G ‐expansion method, direct method, Bäcklund transformation method, auxiliary equation method, Riccati mapping method, and Hirota bilinear transformation method . The Hirota bilinear transformation method is a classical symbolic scheme to seek for the soliton and multiple soliton solutions.…”

Section: Introductionmentioning

confidence: 99%

Analytic rogue wave solutions for a generalized fourth‐order Boussinesq equation in fluid mechanics

2018

Math Methods in App Sciences

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A bilinear transformation method is proposed to find the rogue wave solutions for a generalized fourth-order Boussinesq equation, which describes the wave motion in fluid mechanics. The one-and two-order rogue wave solutions are explicitly constructed via choosing polynomial functions in the bilinear form of the equation. The existence conditions for these solutions are also derived. Furthermore, the system parameter controls on the rogue waves are discussed. The three parameters involved in the equation can strongly impact the wave shapes, amplitudes, and distances between the wave peaks. The results can be used to deeply understand the nonlinear dynamical behaviors of the rogue waves in fluid mechanics.

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Looking at a nonlinear inhomogeneous optical fiber through the generalized higher-order variable-coefficient Hirota equation

Cited by 163 publications

References 38 publications

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations

Analytic rogue wave solutions for a generalized fourth‐order Boussinesq equation in fluid mechanics

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