TY - JOUR
T1 - Waves that Appear From Nowhere
T2 - Complex Rogue Wave Structures and Their Elementary Particles
AU - Akhmediev, Nail
N1 - Publisher Copyright:
© Copyright © 2021 Akhmediev.
PY - 2021/1/15
Y1 - 2021/1/15
N2 - The nonlinear Schrödinger equation has wide range of applications in physics with spatial scales that vary from microns to kilometres. Consequently, its solutions are also universal and can be applied to water waves, optics, plasma and Bose-Einstein condensate. The most remarkable solution presently known as the Peregrine solution describes waves that appear from nowhere. This solution describes unique events localized both in time and in space. Following the language of mariners they are called “rogue waves”. As thorough mathematical analysis shows, these waves have properties that differ them from any other nonlinear waves known before. Peregrine waves can serve as ‘elementary particles’ in more complex structures that are also exact solutions of the nonlinear Schrödinger equation. These structures lead to specific patterns with various degrees of symmetry. Some of them resemble “atomic like structures”. The number of particles in these structures is not arbitrary but satisfies strict rules. Similar structures may be observed in systems described by other equations of mathematical physics: Hirota equation, Davey-Stewartson equations, Sasa-Satsuma equation, generalized Landau-Lifshitz equation, complex KdV equation and even the coupled Higgs field equations describing nucleons interacting with neutral scalar mesons. This means that the ideas of rogue waves enter nearly all areas of physics including the field of elementary particles.
AB - The nonlinear Schrödinger equation has wide range of applications in physics with spatial scales that vary from microns to kilometres. Consequently, its solutions are also universal and can be applied to water waves, optics, plasma and Bose-Einstein condensate. The most remarkable solution presently known as the Peregrine solution describes waves that appear from nowhere. This solution describes unique events localized both in time and in space. Following the language of mariners they are called “rogue waves”. As thorough mathematical analysis shows, these waves have properties that differ them from any other nonlinear waves known before. Peregrine waves can serve as ‘elementary particles’ in more complex structures that are also exact solutions of the nonlinear Schrödinger equation. These structures lead to specific patterns with various degrees of symmetry. Some of them resemble “atomic like structures”. The number of particles in these structures is not arbitrary but satisfies strict rules. Similar structures may be observed in systems described by other equations of mathematical physics: Hirota equation, Davey-Stewartson equations, Sasa-Satsuma equation, generalized Landau-Lifshitz equation, complex KdV equation and even the coupled Higgs field equations describing nucleons interacting with neutral scalar mesons. This means that the ideas of rogue waves enter nearly all areas of physics including the field of elementary particles.
KW - nonlinear schrodinger equation
KW - optical fibers
KW - peregrine wave
KW - rogue waves
KW - water waves
UR - http://www.scopus.com/inward/record.url?scp=85100195724&partnerID=8YFLogxK
U2 - 10.3389/fphy.2020.612318
DO - 10.3389/fphy.2020.612318
M3 - Review article
SN - 2296-424X
VL - 8
JO - Frontiers in Physics
JF - Frontiers in Physics
M1 - 612318
ER -