2002
DOI: 10.1016/s0960-0779(02)00057-7
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A higher-order model for transverse waves in a generalized elastic solid

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Cited by 6 publications
(6 citation statements)
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“…The modulation of transverse waves propagating in a cubically nonlinear and dispersive elastic medium has been considered in a recent study [19] using a multi-scale perturbation method. In this study, the following stretched coordinates are introduced:…”
Section: Wave Modulation Near a Critical Wavenumbermentioning
confidence: 99%
See 1 more Smart Citation
“…The modulation of transverse waves propagating in a cubically nonlinear and dispersive elastic medium has been considered in a recent study [19] using a multi-scale perturbation method. In this study, the following stretched coordinates are introduced:…”
Section: Wave Modulation Near a Critical Wavenumbermentioning
confidence: 99%
“…Substituting solutions (8) together with the stretched coordinates ( 7) into the governing equations ( 5), a hierarchy of equations in terms of powers of is obtained. Solutions of the perturbation equations lead to the compatibility conditions in the form of a pair of two coupled nonlinear Schödinger equations [19]…”
Section: Wave Modulation Near a Critical Wavenumbermentioning
confidence: 99%
“…Motivated by this work, the algorithmic procedure of the preceding sections is applied mutatis mutandis to a single component but modulated NLS equation which describes the transmission of transverse waves through incompressible hyperelastic media under rotation [24]. This work is preparatory to a projected later investigation into potential extension of the algorithmic procedure to Manakov-type systems that arise in nonlinear elasticity (see, e.g., [25]).…”
Section: Incompressible Hyperelastic Solidsmentioning
confidence: 99%
“…Denklemi (4)'deki üst çizgi ile ifade edilen fonksiyon karmaşık eşleniği göstermektedir. Daha sonra Hacinliyan ve Erbay, genelleştirilmiş elastik bir ortamda aynı anda yayılan iki kısa enine dalganın modülasyon probleminde yüksek mertebe doğrusal olmayan ve dispersiyonun etkilerini araştırmışlar ve denklem (4)'ü kuple denklem sisteminde elde etmişlerdir [17]. Akhatov ve Khismatullin ise kabarcıklı sıvılarda kısa dalga ve uzun dalga etkileşim problemini incelemişler ve yüksek mertebe etkileri içeren uzun dalga ve kısa dalga denklemlerini hesaplamışlardır [18].…”
Section: Introductionunclassified