Nonlinear elastodynamics of materials with strong ellipticity condition: Carroll-type solutions

Rogers, C.; Saccomandi, Giuseppe; Vergori, Luigi

doi:10.1016/j.wavemoti.2015.02.009

Cited by 12 publications

(3 citation statements)

References 27 publications

(34 reference statements)

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“…For consistency of the model (4.14) with linear elasticity in the limit of small strains, it is necessary that 15) µ 0 being the infinitesimal shear modulus, while requiring that (4.14) meets the the strong ellipticity condition implies that (see Ref. [46] for details)…”

Section: Transverse Wave Propagation In Hyperelastic Materialsmentioning

confidence: 99%

Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction

Rogers¹,

Saccomandi²,

Vergori³

2021

JNMP

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Nonlinear Schrödinger equations with spatial modulation associated with integrable Hamiltonian systems of Ermakov-Ray-Reid type are introduced. An algorithmic procedure is presented which exploits invariants of motion to construct exact wave packet representations with potential applications in a wide range of physical contexts such as, 'inter alia', the analysis of Bloch wave and matter wave solitonic propagation and pulse transmission in Airy modulated NLS models. A particular Ermakov reduction for Mooney-Rivlin materials is set in the broader context of transverse wave propagation in a class of higher-order hyperelastic models of incompressible solids.

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Section: Transverse Wave Propagation In Hyperelastic Materialsmentioning

confidence: 99%

Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction

Rogers¹,

Saccomandi²,

Vergori³

2021

JNMP

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“…A massive longitudinal wave equation can then be written from the nonlinear theory that would give the parallel displacements of constituent finite spacetime parcels with zero spacing between them. Analogous to the model of a lattice phonon as the vibratory motion of a particle continuum, the Dilation field can be described very much like the phononic model with appropriate modifications for a classical field [8,9]. With this, spacetime fluidity can be described by a collection of local unit volumes with mass m vac .…”

Section: B Lagrangian Density Of the Dilation Fieldmentioning

confidence: 99%

“…This tensor field is also predicted to interact with the massive background spacetime and itself, thus we include nonlinear interaction terms in L m up to order-σ and coupled by a constant (g σ ) that accounts for the strength of the field-field and fieldbackground coupling. [9,12,13]…”

Section: B Lagrangian Density Of the Dilation Fieldmentioning

confidence: 99%

Scalar-Tensor Gravitational Strain Field Equations and the Longitudinal Wave Form

Gamble¹,

Flurchick²

2018

Preprint

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From modern observations of gravitational interactions, it can be inferred that there is much left to discover about the fundamental gravitational field. Since the advent of the General Theory of Relativity over a century ago, we have come to make exotic assumptions pertaining to the inner workings of an associated field theory. One of which is an elastic nature to spacetime and the behavior of gravity for strong and weak fields. In this work we investigate a more physical nature, expanding upon general relativity led by observations of strong sources. We introduce a candidate Lorentz-invariant field theory that employs an elastic and pseudoscalar nature to the field interpretation and it's properties. A unique generation of the Euler-Lagrange equations of motion is presented; resulting in a longitudinal wave equation for the Dilation gravitational field. This provides a modern advancement of a relativistic gravitational field theory, supported by observation.

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