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A new equation and exact solutions describing focal fields in media with modular nonlinearity
Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för maskinteknik. Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för maskinteknik.
Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för maskinteknik. Blekinge Tekniska Högskola, Sektionen för teknik, Avdelningen för matematik och naturvetenskap. Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för maskinteknik. Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för matematik och naturvetenskap. Blekinge Tekniska Högskola, Institutionen för telekommunikation och matematik.ORCID-id: 0000-0001-8739-4492
2017 (engelsk)Inngår i: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 89, nr 3, s. 1905-1913Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Brand-new equations which can be regarded as modifications of Khokhlov–Zabolotskaya–Kuznetsov or Ostrovsky–Vakhnenko equations are suggested. These equations are quite general in that they describe the nonlinear wave dynamics in media with modular nonlinearity. Such media exist among composites, meta-materials, inhomogeneous and multiphase systems. These new models are interesting because of two reasons: (1) the equations admit exact analytic solutions and (2) the solutions describe real physical phenomena. The equations model nonlinear focusing of wave beams. It is shown that inside the focal zone a stationary waveform exists. Steady-state profiles are constructed by the matching of functions describing the positive and negative branches of exact solutions of an equation of Klein–Gordon type. Such profiles have been observed many times during experiments and numerical studies. The non-stationary waves can contain singularities of two types: discontinuity of the wave and of its derivative. These singularities are eliminated by introducing dissipative terms into the equations—thereby increasing their order. © 2017 The Author(s)

sted, utgiver, år, opplag, sider
Springer Netherlands , 2017. Vol. 89, nr 3, s. 1905-1913
Emneord [en]
Bimodular media, Exact solution, Focusing, HIFU, High-intensity focused ultrasound, Modified KZ–OV, Modular nonlinearity, Nonlinear partial differential equation, Control nonlinearities, Partial differential equations, High intensity focused ultrasound, Nonlinear partial differential equations, Nonlinear equations
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URN: urn:nbn:se:bth-14471DOI: 10.1007/s11071-017-3560-8ISI: 000405962800025Scopus ID: 2-s2.0-85019632379OAI: oai:DiVA.org:bth-14471DiVA, id: diva2:1108780
Tilgjengelig fra: 2017-06-13 Laget: 2017-06-13 Sist oppdatert: 2017-08-22bibliografisk kontrollert

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