Soliton solutions for perturbed Radhakrishnan-Kundu-Lakshmanan equation

Abstract

To find some soliton solutions of the equation, the perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation has been considered. For this purpose, GKM (generalized Kudryashov method), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been applied to the perturbed RKL equation. First, considered the nonlinear partial differential equation, is reduced to an ordinary differential equation with the help of the traveling wave transformation. Afterward, obtained the algebraic equation system through the balance principle was solved with the help of Wolfram Mathematica 12. Thus, some new soliton solutions of the discussed equation have been obtained. Both 2D and 3D graphics have been drawn with the help of Wolfram Mathematica 12 by giving some values to obtained these new solutions.

Keywords

• GKM
• perturbed RKL equation
• soliton solutions

Perturbe edilmiş Radhakrishnan-Kundu-Lakshmanan denklemi için soliton çözümler

Abstract

Denklemin bazı soliton çözümlerini bulmak için perturbe edilmiş Radhakrishnan-Kundu-Lakshmanan (RKL) denklemi ele alınmıştır. Bu amaç için lineer olmayan evrim denklemleri (NLEEs)’nin çözüm yöntemlerinden biri olan GKM (genelleştirilmiş Kudryashov metodu), perturbe edilmiş RKL denklemine uygulanmıştır. İlk olarak ele alınan lineer olmayan kısmi diferansiyel denklem, hareketli dalga dönüşümü yardımıyla bir adi diferansiyel denkleme indirgenmiştir. Daha sonra denge prensibi ile elde edilen cebirsel denklem sistemi Wolfram Mathematica 12 yardımıyla çözülmüştür. Böylece ele alınmış olan denklemin bazı yeni soliton çözümleri elde edilmiştir. Elde edilen bu yeni çözümlere birtakım değerler verilerek Wolfram Mathematica 12 yardımıyla hem 2 boyutlu hem de 3 boyutlu grafiklerin çizimleri yapılmıştır

Keywords

• GKM
• perturbe edilmiş RKL denklemi
• soliton çözümler

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