Self-localized solitons of the nonlinear wave blocking problem

Bayındır C.

DYNAMICS OF ATMOSPHERES AND OCEANS, cilt.93, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 93
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.dynatmoce.2020.101189
  • Dergi Adı: DYNAMICS OF ATMOSPHERES AND OCEANS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Environment Index, INSPEC, Metadex, Civil Engineering Abstracts
  • Anahtar Kelimeler: Nonlinear wave blocking, Smith's nonlinear Schrodinger equation, Spectral renormalization method, Soliton stability
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

In this paper, we propose a numerical framework to study the shapes, dynamics, and stabilities of the self-localized solutions of the nonlinear wave blocking problem. To our best knowledge, blocking of the solitons in the marine environment has not been studied before in the existing literature. With this motivation, we use the nonlinear Schrodinger equation (NLSE) derived by Smith as a model for the nonlinear wave blocking. We propose a spectral renormalization method (SRM) to find the self-localized solitons of this model. We show that for constant, linearly varying or sinusoidal current gradient, i.e. dU/dx, the self-localized solitons of the Smith's NLSE do exist. Additionally, we propose a spectral scheme with a 4th order Runge-Kutta time integrator to study the temporal dynamics and stabilities of such solitons. We observe that self-localized solitons are stable for the cases of constant or linearly varying current gradient however, they are unstable for sinusoidal current gradient, at least for the selected parameters. We comment on our findings and discuss the importance and applicability of the proposed approach.