Single-peak solitary wave solutions for the generalized Korteweg–de Vries equation

Ma, Li; Li, Hong; Ma, Jun

doi:10.1007/s11071-014-1668-7

Cited by 6 publications

(2 citation statements)

References 24 publications

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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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Section: Introductionmentioning

confidence: 99%

On the compact wave dynamics of tensegrity beams in multiple dimensions

Micheletti

Ruscica

2019

Nonlinear Dyn

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“…Here we just mention some of the recent work. Biswas [5] studied the solitary wave solution for KdV equation with power law nonlinearity and time-dependent coefficients, [6] investigated the solitons, shock waves for the potential KdV equation, while [7] studied the solitary wave solutions for the generalized KdV equation. In addition to the theoretical studies, readers can refer to [8,9] for the numerical simulations of the KdV equation and the generalized KdV equation.…”

Section: Introductionmentioning

confidence: 99%

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

2015

Nonlinear Dyn

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Recently, Biswas et al. (Phys Wave Phenom 19:24-29, 2011) derived exact bright and dark solitary solutions for the Rosenau-Kawahara equation with power law nonlinearity, and Hu et al. (Adv Math Phys 11, Article ID 217393, 2014) proposed two conservative finite difference schemes for the usual RosenauKawahara equation. In this paper, we obtain another set of exact solitary solutions for the Rosenau-Kawahara equation with power law nonlinearity. More importantly, a conservative finite difference method is presented. The fundamental energy conservation law is preserved by the current numerical scheme. And the existence and uniqueness of the numerical solution are proved. The convergence and stability of the numerical solution are also shown. The method is second-order convergent both in time and in space. Finally, numerical results confirm well with the theoretical results and show that the current method can be well used to study the solitary wave at long time.

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Exact solitary solution and a three-level linearly implicit conservative finite difference method for the generalized Rosenau–Kawahara-RLW equation with generalized Novikov type perturbation

2016

Nonlinear Dyn

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Single-peak solitary wave solutions for the generalized Korteweg–de Vries equation

Cited by 6 publications

References 24 publications

On the compact wave dynamics of tensegrity beams in multiple dimensions

On the compact wave dynamics of tensegrity beams in multiple dimensions

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

Exact solitary solution and a three-level linearly implicit conservative finite difference method for the generalized Rosenau–Kawahara-RLW equation with generalized Novikov type perturbation

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