Theory of Nonlinear Surface Waves and Solitons

Maugin, Gérard A.

doi:10.1007/3-211-38065-5_7

Cited by 6 publications

(2 citation statements)

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“…There may also be abuses in the consideration of the BO-KdV equation in modeling some physical problems. This is the case with nonlinear surface wave propagation for seismic purposes [54], which in fact requires a much more careful and complicated modeling (in particular to account for the typical in-depth (transverse) behavior of a surface wave over a solid complex structure [55].…”

Section: Discussionmentioning

confidence: 99%

On Boussinesq's paradigm in nonlinear wave propagation

Christov

Maugin

Порубов

2007

Comptes Rendus. Mécanique

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Boussinesq's original derivation of his celebrated equation for surface waves on a fluid layer opened up new horizons that were to yield the concept of the soliton. The present contribution concerns the set of Boussinesq-like equations under the general title of 'Boussinesq's paradigm'. These are true bi-directional wave equations occurring in many physical instances and sharing analogous properties. The emphasis is placed: (i) on generalized Boussinesq systems that involve higher-order linear dispersion through either additional space derivatives or additional wave operators (so-called double-dispersion equations); and (ii) on the 'mechanics' of the most representative localized nonlinear wave solutions. Dissipative cases and two-dimensional generalizations are also considered.

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Section: Discussionmentioning

confidence: 99%

On Boussinesq's paradigm in nonlinear wave propagation

Christov

Maugin

Порубов

2007

Comptes Rendus. Mécanique

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“…They have generally worked on topics such as the existence of various types of nonlinear surface waves, the possibility of the existence of solitary waves as a result of balancing between dispersion and nonlinearity, the solution of nonlinear evaluation equations including Korteweg-de Vries (K-DV), nonlinear Schrödinger (NLS), Boussinesq (BE), and so on. To mention all is impossible but at least some of these scientific articles, reviews, and books can be cited as [19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Studies on Love Waves. Part 1. Nonlinear Modulation of Love Waves on a Heterogeneous Half-Space covered by a Homogeneous Layer

Demirkuş

2022

Preprint

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The aim of this paper is, analytically, to deal with the nonlinear modulation of Love waves in a single-layered half-space. In this study, the propagation of Love waves on a solid half-space covered by a solid layer is considered. Both mediums contain nonlinear, isotopic, hyper-elastic, and generalized neo-Hookean materials. Additionally, the layer consists of homogeneous materials and the half-space involves heterogeneous materials. Heterogeneity varies with the thickness and is uniform in any direction parallel to the boundaries. Furthermore, the upper surface to be free from traction, and displacements and stresses to be continuous at the interface are assumed, in addition to holding the radiation condition in the half-space. It is noted that this problem corresponds to the improved version of Love wave propagation. An improvement is from linear to nonlinearity and from homogeneity to heterogeneity. Therefore, in this work, the improved version of Love wave dispersion is obtained. In addition, the nonlinear modulation of Love waves is given by the nonlinear Schrödinger equation. Moreover, the possibility of the existence of solitary waves, as a result of balancing between dispersion and nonlinearity, is investigated.

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