Soliton solutions to the Sawada–Kotera equation

Aktosun T., Choque-Rivero A. E., Toledo I., ÜNLÜ M.

Analysis and Mathematical Physics, AMP 2024, Virtual, Online, Meksika, 5 - 17 Ağustos 2024, ss.1-33, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Doi Numarası: 10.1515/9783111579313-001
  • Basıldığı Şehir: Virtual, Online
  • Basıldığı Ülke: Meksika
  • Sayfa Sayıları: ss.1-33
  • Anahtar Kelimeler: bound-state dependency constants, Inverse scattering for the third-order equation, Sawada–Kotera equation, soliton solutions
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

We consider the direct and inverse scattering problems for the third-order differential equation in the reflectionless case. We formulate a corresponding Riemann–Hilbert problem using input consisting of the bound-state poles of a transmission coefficient and the bound-state dependency constants. With the time-evolved dependency constants, using the solution to the Riemann–Hilbert problem, we construct soliton solutions to a certain integrable system of fifth-order nonlinear partial differential equations. By imposing some appropriate restrictions on the dependency constants, we show that those soliton solutions yield soliton solutions to the Sawada–Kotera equation.