On symmetries and conservation laws of the Majda–Biello system

Vodova-Jahnova, Jirina

doi:10.1016/j.nonrwa.2014.08.005

Cited by 7 publications

(3 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…R S U (η)dη −15.37 (see figure 10 wave turbulence [25]. Interestingly [26] points out our Biello-Majda system has only these four conserved quantities.…”

Section: Comparison To Numerical Simulationsmentioning

confidence: 86%

Multiple-scale analysis on the radiation within the coupled KdV equations

Li¹,

Biello²,

Li³

2016

Preprint

View full text Add to dashboard Cite

A multiple scale model of the nonlinearly coupled KdV equations is established to predict mechanism of interaction of equatorial Rossby waves and barotropic waves in certain case. Analytically, predicted precursor radiation is a centrosymmetric object and is shown in excellent quantitative agreement with numerical simulations; furthermore, the multiple scale model elucidates the salient mechanisms of the interaction of solitary waves and the mechanism for radiation. While the atmosphere-ocean science community is very interested in theoretical studies of tropical wave interactions and in developing reduced dynamical models that can explain some key features of equatorial phenomena, our analytic predictions quantitively explain formation of radiation during interaction in Biello's model beyond qualitative level.

show abstract

“…R S U (η)dη −15.37 (see figure 10 wave turbulence [25]. Interestingly [26] points out our Biello-Majda system has only these four conserved quantities.…”

Section: Comparison To Numerical Simulationsmentioning

confidence: 86%

Multiple-scale analysis on the radiation within the coupled KdV equations

Li¹,

Biello²,

Li³

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…We believe that using the technique similar to that of [43] (cf. also [20,44]) it can be shown that in the case of n = −5 equation (13) admits no genuinely generalized symmetries, including those with explicit dependence on T and not just the time-independent ones whose nonexistence follows from the above comparison of (15) with (23), so we are left with just one integrable case of n = −2 which we discuss below.…”

Section: Integrabilitymentioning

confidence: 99%

Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules

Sergyeyev

Skurativskyi

Vladimirov

2019

Nonlinear Analysis: Real World Applications

View full text Add to dashboard Cite

We present the results of study of a nonlinear evolutionary PDE (more precisely, a oneparameter family of PDEs) associated with the chain of pre-stressed granules. The PDE in question supports solitary waves of compression and rarefaction (bright and dark compactons) and can be written in Hamiltonian form. We investigate inter alia integrability properties of this PDE and its generalized symmetries and conservation laws.For the compacton solutions we perform a stability test followed by the numerical study. In particular, we simulate the temporal evolution of a single compacton, and the interactions of compacton pairs. The results of numerical simulations performed for our model are compared with the numerical evolution of corresponding Cauchy data for the discrete model of chain of pre-stressed elastic granules.

show abstract

“…However, unlike the KdV, the system is not completely integrable, even in the relatively simple case α = 1. It was recently shown by Vodová-Jahnová that there are no higher conservation laws [30]. The system scales like the KdV, leading to a critical Sobolev index of − 3 2 .…”

Section: Introductionmentioning

confidence: 98%

Smoothing and Global Attractors for the Majda-Biello System on the Torus

Compaan¹

2015

Preprint

View full text Add to dashboard Cite

In this paper, we consider the Majda-Biello system, a coupled KdV-type system, on the torus. In the first part of the paper, it is shown that, given initial data in a Sobolev space, the difference between the linear and the nonlinear evolution almost always resides in a smoother space. The smoothing index depends on number-theoretic properties of the coupling parameter in the system which control the behavior of the resonant sets.In the second part of the paper, we consider the forced and damped version of the system and obtain similar smoothing estimates. These estimates are used to show the existence of a global attractor in the energy space. We also show that when the damping is large in relation to the forcing terms, the attractor is trivial.

show abstract

On symmetries and conservation laws of the Majda–Biello system

Cited by 7 publications

References 45 publications

Multiple-scale analysis on the radiation within the coupled KdV equations

Multiple-scale analysis on the radiation within the coupled KdV equations

Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules

Smoothing and Global Attractors for the Majda-Biello System on the Torus

Contact Info

Product

Resources

About