Exact solitons, periodic peakons and compactons in an optical soliton model

Zhang, Tonghua; Li, Jibin

doi:10.1007/s11071-017-3950-y

Cited by 7 publications

(2 citation statements)

References 12 publications

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“…However, different from the aforementioned methods [16][17][18][19][20][21][22][23][24], in this paper, we apply the dynamical system method to study the bifurcation and exact solutions of NPDEs. Dynamical system method is quite different from the mentioned methods, and it has many successful applications [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Another purpose is to study exact solutions of the fractional-order Wu-Zhang system [16].…”

Section: Introductionmentioning

confidence: 99%

Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis

Zheng

Xia

Bai

et al. 2020

Discrete Dynamics in Nature and Society

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In this paper, based on the dynamical system method, we obtain the exact parametric expressions of the travelling wave solutions of the Wu–Zhang system. Our approach is much different from the existing literature studies on the Wu–Zhang system. Moreover, we also study the fractional derivative of the Wu–Zhang system. Finally, by comparison between the integer-order Wu–Zhang system and the fractional-order Wu–Zhang system, we see that the phase portrait, nonzero equilibrium points, and the corresponding exact travelling wave solutions all depend on the derivative order α. Phase portraits and simulations are given to show the validity of the obtained solutions.

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Section: Introductionmentioning

confidence: 99%

Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis

Zheng

Xia

Bai

et al. 2020

Discrete Dynamics in Nature and Society

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“…Particularly interesting is the case of solitons with finite span (or wavelenegth)-usually refereed to as 'compactons' [18]. Solitary waves characterized by different, symmetric, antisymmetric, and cusped profiles are actively investigated in the literature [19,20,21], which is also populated by multifaceted studies on the stability of such waves [20,22,23]. From the engineering point of view, solitary wave dynamics has been proven to be useful for the construction of a variety of novel acoustic devices, including: acoustic band gap materials; shock protector devices; acoustic lenses; and energy trapping containers (refer, e.g., to [6] and references therein).…”

Section: Introductionmentioning

confidence: 99%

On the compact wave dynamics of tensegrity beams in multiple dimensions

Micheletti

Ruscica

2019

Nonlinear Dyn

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This work presents a numerical investigation on the nonlinear wave dynamics of tensegrity beams in 1D, 2D and 3D arrangements. The simulation of impact loading on a chain of tensegrity prisms and lumped masses allows us to apply on a smaller scale recent results on the propagation of compression solitary waves in 1D tensegrity metamaterials. Novel results on the wave dynamics of 2D and 3D beams revealfor the first time -the presence of compact compression waves in two-and three-dimensional tensegrity lattices with slender aspect ratio. The dynamics of such systems is characterized by the thermalization of the lattice nearby the impacted regions of the boundary. The portion of the absorbed energy moving along the longitudinal direction is transported by compression waves with compact support. Such waves emerge with nearly constant speed, and slight modifications of their spatial shape and amplitude, after collisions with compression waves traveling in opposite direction. The analyzed behaviors suggest the use of multidimensional tensegrity lattices for the design and additive manufacturing of novel sound focusing devices.

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Series solutions and bifurcation of traveling waves in the Benney–Kawahara–Lin equation

Zhou

Liu

2019

Nonlinear Dyn

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Exact solitons, periodic peakons and compactons in an optical soliton model

Cited by 7 publications

References 12 publications

Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis

Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis

On the compact wave dynamics of tensegrity beams in multiple dimensions

Series solutions and bifurcation of traveling waves in the Benney–Kawahara–Lin equation

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