Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Benjamin-Ono-related equations and their solutions.

K M Case1

  • 1Physics Department, The Rockefeller University, New York, New York 10021.

Proceedings of the National Academy of Sciences of the United States of America
|January 1, 1979
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Constants and pseudo-constants of the Kadomtsev-Petviashvili equation.

Proceedings of the National Academy of Sciences of the United States of America·1985
Same author

A theorem about Hamiltonian systems.

Proceedings of the National Academy of Sciences of the United States of America·1984
Same author

Canonical coordinates for plasma and hydrodynamic problems.

Proceedings of the National Academy of Sciences of the United States of America·1981
Same author

Bäcklund transformations for multidimensional sine-Gordon equations.

Proceedings of the National Academy of Sciences of the United States of America·1980
Same author

Conserved densities.

Proceedings of the National Academy of Sciences of the United States of America·1980
Same author

The N-soliton solution of the Benjamin-Ono equation.

Proceedings of the National Academy of Sciences of the United States of America·1978
Same journal

Chemotactic self-organization captures the dynamics of mammalian hair follicle patterning.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Tomographic imaging of superconducting order using particle-hole interference.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Inhibitory potential of autologous neutralizing antibodies sets quantitative limits on the rebound-competent HIV-1 reservoir.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Inferring epidemiological parameters under an infectious phylogeography model with visitor dynamics.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Analytical modeling for suction cup designs for skin-interfaced wearable devices.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Improving cell-free metabolism through direct integration of artificial respiratory chains.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

The Benjamin-Ono equation, a nonlinear singular integral equation, is part of a larger hierarchy. Researchers constructed explicit multisoliton solutions for all equations within this hierarchy.

Area of Science:

  • Nonlinear Partial Differential Equations
  • Mathematical Physics
  • Soliton Theory

Background:

  • The Benjamin-Ono equation is a significant model in fluid dynamics and nonlinear wave phenomena.
  • It belongs to a hierarchy of integrable equations, suggesting rich mathematical structures.
  • Understanding its solutions is crucial for analyzing complex wave interactions.

Purpose of the Study:

  • To establish the Benjamin-Ono equation's position within a hierarchy of nonlinear singular integral equations.
  • To derive explicit multisoliton solutions for all equations in this hierarchy.
  • To provide a comprehensive analytical framework for these nonlinear systems.

Main Methods:

  • Classification of the Benjamin-Ono equation within a hierarchy of nonlinear partial differential singular integral equations.

Related Experiment Videos

  • Development of analytical techniques for constructing exact solutions.
  • Application of methods for generating multisoliton solutions.

    • Main Results:

    • The Benjamin-Ono equation is confirmed as a member of a specific hierarchy.
    • Explicit formulas for multisoliton solutions are successfully derived for the entire hierarchy.
    • The findings offer precise descriptions of complex wave behaviors.

    Conclusions:

    • The study successfully places the Benjamin-Ono equation within its hierarchical context.
    • Explicit multisoliton solutions are now available for the entire hierarchy, advancing the field.
    • This work provides a fundamental contribution to the understanding of nonlinear singular integral equations.