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Article: Breathers, cascading instabilities and Fermi–Pasta–Ulam–Tsingou recurrence of the derivative nonlinear Schrödinger equation: Effects of ‘self-steepening’ nonlinearity
Title | Breathers, cascading instabilities and Fermi–Pasta–Ulam–Tsingou recurrence of the derivative nonlinear Schrödinger equation: Effects of ‘self-steepening’ nonlinearity |
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Authors | |
Keywords | Breathers Cascading instability Derivative nonlinear Schrödinger equation Fermi–Pasta–Ulam–Tsingou recurrence |
Issue Date | 2021 |
Publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/physd |
Citation | Physica D: Nonlinear Phenomena, 2021, v. 428, article no. 133033 How to Cite? |
Abstract | Breathers, modulation instability and recurrence phenomena are studied for the derivative nonlinear Schrödinger equation, which incorporates second order dispersion, cubic nonlinearity and self-steepening effect. By insisting on periodic boundary conditions, a cascading process will occur where initially small higher order Fourier modes can grow alongside with lower order modes. Typically a breather is first observed when all modes attain roughly the same order of magnitude. Beyond the formation of the first breather, analytical formula of spatially periodic but temporally localized breather ceases to be a valid indicator. However, numerical simulations display Fermi–Pasta–Ulam–Tsingou type recurrence. Self-steepening effect plays a crucial role in the dynamics, as it induces motion of the breather and generates chaotic behavior of the Fourier coefficients. Theoretically, correlation between breather motion and the Lax pair formulation is made. Physically, quantitative assessments of wave profile evolution are made for different initial conditions, e.g. random noise versus modulation instability mode of maximum growth rate. Potential application to fluid mechanics is discussed. |
Persistent Identifier | http://hdl.handle.net/10722/307878 |
ISSN | 2023 Impact Factor: 2.7 2023 SCImago Journal Rankings: 1.074 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Yin, HM | - |
dc.contributor.author | Chow, KW | - |
dc.date.accessioned | 2021-11-12T13:39:13Z | - |
dc.date.available | 2021-11-12T13:39:13Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Physica D: Nonlinear Phenomena, 2021, v. 428, article no. 133033 | - |
dc.identifier.issn | 0167-2789 | - |
dc.identifier.uri | http://hdl.handle.net/10722/307878 | - |
dc.description.abstract | Breathers, modulation instability and recurrence phenomena are studied for the derivative nonlinear Schrödinger equation, which incorporates second order dispersion, cubic nonlinearity and self-steepening effect. By insisting on periodic boundary conditions, a cascading process will occur where initially small higher order Fourier modes can grow alongside with lower order modes. Typically a breather is first observed when all modes attain roughly the same order of magnitude. Beyond the formation of the first breather, analytical formula of spatially periodic but temporally localized breather ceases to be a valid indicator. However, numerical simulations display Fermi–Pasta–Ulam–Tsingou type recurrence. Self-steepening effect plays a crucial role in the dynamics, as it induces motion of the breather and generates chaotic behavior of the Fourier coefficients. Theoretically, correlation between breather motion and the Lax pair formulation is made. Physically, quantitative assessments of wave profile evolution are made for different initial conditions, e.g. random noise versus modulation instability mode of maximum growth rate. Potential application to fluid mechanics is discussed. | - |
dc.language | eng | - |
dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/physd | - |
dc.relation.ispartof | Physica D: Nonlinear Phenomena | - |
dc.subject | Breathers | - |
dc.subject | Cascading instability | - |
dc.subject | Derivative nonlinear Schrödinger equation | - |
dc.subject | Fermi–Pasta–Ulam–Tsingou recurrence | - |
dc.title | Breathers, cascading instabilities and Fermi–Pasta–Ulam–Tsingou recurrence of the derivative nonlinear Schrödinger equation: Effects of ‘self-steepening’ nonlinearity | - |
dc.type | Article | - |
dc.identifier.email | Yin, HM: hmy63110@hku.hk | - |
dc.identifier.email | Chow, KW: kwchow@hku.hk | - |
dc.identifier.authority | Chow, KW=rp00112 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.physd.2021.133033 | - |
dc.identifier.scopus | eid_2-s2.0-85117215254 | - |
dc.identifier.hkuros | 329516 | - |
dc.identifier.volume | 428 | - |
dc.identifier.spage | article no. 133033 | - |
dc.identifier.epage | article no. 133033 | - |
dc.identifier.isi | WOS:000710502400009 | - |
dc.publisher.place | Netherlands | - |