Partial differential equations that lead to solitons

Kaya D.

Encyclopedia of Complexity and Systems Science Series, Mohamed Atef Helal, Editör, Springer Nature, New York, ss.193-201, 2022

  • Yayın Türü: Kitapta Bölüm / Diğer
  • Basım Tarihi: 2022
  • Yayınevi: Springer Nature
  • Basıldığı Şehir: New York
  • Sayfa Sayıları: ss.193-201
  • Editörler: Mohamed Atef Helal, Editör
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

Abstract

In this part, we introduce the reader to a certain class of nonlinear partial differential equations which are characterized by solitarywave solutions of the classical nonlinear equations that lead tosolitons. The classical nonlinear equations of interest show the existence of special types of travelingwave solutions which are either solitary waves or solitons. In this study, we will review a few solutions arising from the analytic work of theKorteweg–de Vries (KdV) equations, the generalized regularized long-wave RLW equation, Kadomtsev–Petviashvili (KP) equation, theKlein–Gordon (KG) equation, the Sine-Gordon (SG) equation, the Boussinesq equation, Pochhammer–Chree (PC) equation and the nonlinearSchrödinger (NLS) equation, the Fisher equation, Burgers equation, the Korteweg–de Vries Burgers’ equation (KdVB), the two-dimensionalKorteweg-deVries Burgers’ (tdKdVB), the potential Kadomtsev–Petviashvili equation, the Kawahara equation, Generalized Zakharov-Kuznetsov (gZK)equation, the Sharma-Tasso-Olver equation, and the Cahn–Hilliard equation.