Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
A new equation and exact solutions describing focal fields in media with modular nonlinearity
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science. Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences. Blekinge Institute of Technology, Department of Telecommunications and Mathematics.ORCID iD: 0000-0001-8739-4492
2017 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, 1-9 p.Article in journal (Refereed) Epub ahead of print
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)

Place, publisher, year, edition, pages
Springer Netherlands , 2017. 1-9 p.
Keyword [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
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:bth-14471DOI: 10.1007/s11071-017-3560-8Scopus ID: 2-s2.0-85019632379OAI: oai:DiVA.org:bth-14471DiVA: diva2:1108780
Available from: 2017-06-13 Created: 2017-06-13 Last updated: 2017-06-13

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Rudenko, OlegHedberg, Claes
By organisation
Department of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mathematics and ScienceDepartment of Mathematics and Natural SciencesDepartment of Telecommunications and Mathematics
In the same journal
Nonlinear dynamics
Other Materials Engineering

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 3 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf