Single soliton and double soliton solutions of the quadratic-nonlinear Korteweg-de Vries equation for small and long-times

BAŞHAN A., ESEN A.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, cilt.37, sa.2, ss.1561-1582, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1002/num.22597
  • Dergi Adı: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1561-1582
  • Anahtar Kelimeler: B-spline, differential quadrature method, finite difference method, KdV equation, soliton, CUBIC B-SPLINES, KDV EQUATION, DIFFERENTIAL QUADRATURE, NUMERICAL-SOLUTIONS, FINITE-DIFFERENCE, BURGERS-EQUATION, WAVE SOLUTIONS, COLLOCATION
  • İnönü Üniversitesi Adresli: Evet

Özet

In this article, numerical solutions of the seven different forms of the single soliton and double soliton solutions of the Korteweg-de Vries equation are investigated. Since numerical solution of the six test problems for small-times do not exist in the literature, the present numerical results firstly are reported with exact solutions. Besides small-time solutions, long-time solutions of all test problems are obtained and compared with some of the earlier works. Present algorithm which is based on combination of finite difference method and differential quadrature method have obtained superior results than those in the given literature. Numerical and exact solutions for small-time of all test problems are plotted together for all test problems. Since the numerical results are too close to exact solutions the graphs are indistinguishable. Numerical simulations for long-time solutions are plotted and the error graphs are plotted for the end of the simulations of all test problems.