On the investigation of chiral solitons via modified new Kudryashov method

ÖZIŞIK M., SEÇER A., Bayram M.

International Journal of Geometric Methods in Modern Physics, vol.20, no.7, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 7
  • Publication Date: 2023
  • Doi Number: 10.1142/s0219887823501177
  • Journal Name: International Journal of Geometric Methods in Modern Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Soliton, current density, internal self-potential, bright soliton, the new Kudryashov method
  • Yıldız Technical University Affiliated: Yes


Purpose: This study includes the examination of the cases where the (1 + 1)-dimensional chiral nonlinear Schrödinger equation also has Bohm potential. This review is not to obtain different soliton solutions for both cases but to obtain a certain type of soliton and to observe the effect of the problem parameters. By using the modified new Kudryashovs scheme. This observation also includes how the soliton behavior is effective by comparing the (1 + 1)-dimensional chiral nonlinear Schrödinger equation (C-NLSE) and (1 + 1)-dimensional chiral nonlinear Schrödinger equation with Bohm potential (C-NLSE-BP), especially by examining the Bohm potential parameter. Methodology: In order to apply the proposed analytical method which is the modified Kudryasovs scheme (m-NKM), as in many studies, the nonlinear partial ordinary differential equation (NLPDE) is first converted into nonlinear ordinary differential equation form (NLODE) by using wave transform. Then, in order to determine which degree the solution function to be proposed will be, the balancing constant is calculated. The next step is to determine the unknown parameters of the problem by applying the m-NKM on NODE, obtaining solution sets, and combine the solution of the Riccati equation, which is the basis of the method, with the proposed solution function and wave transform. Obtaining the optical solution by providing the main NLPDE is the next step that follows this stage. The final stage is the graphical analysis and interpretation of the parameter effect for both problems using the obtained solution function. Findings: The examination of the case with and without Bohm potential was carried out on the behavior of the bright soliton shape, which is one of the basic soliton shapes that many effects can be clearly studied on it. It was successfully shown that both equation parameters and the Bohm potential had a significant effect on the soliton behavior, graphical presentations were made and interpreted in detail. Originality: Such an examination has not been studied before in the literature for the investigated equations.