Lump-soliton interaction solutions to differential-difference mKdV systems in (2+1)-dimensions

• Published in: Results in physics 2024-04, Vol.59, p.107579, Article 107579
• Main Authors: Zhou, Kai, Hu, Ya-Nan, Peng, Jun-Da, Shi, Kai-Zhong, Shen, Shou-Feng, Ma, Wen-Xiu
• Format: Article
• Language: English
• Subjects: Differential-difference mKdV equation; Fission\fusion phenomena; Fissionusion phenomena; Hirota’s bilinear operator method; Lump-soliton interaction solution
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2024.107579

Lump-soliton interaction solutions to continuous integrable systems have been pretty well studied, but there are relatively few results in the differential-difference (DΔ) case. In this paper, some (2+1)-dimensional DΔ-mKdV systems are investigated by using Hirota’s bilinear operator method. By setting appropriate variable transformations and assuming auxiliary functions as quadratic and exponential functions, lump-soliton interaction solutions are derived. Certain fission∖fusion phenomena of the physical quantity, the velocity of the potential, are explored by analyzing dynamical behaviors of the resultant solutions with different values of the involved parameters. •Lump-soliton interaction solutions of some (2+1)-dimensional differential-difference-mKdV systems are constructed for the first time.•Because of the use of Hirota’s bilinear operator, this direct ansatz method can be easily applied to other equations.•New fission∖fusion phenomena are explored by analyzing dynamical behaviors of the resultant solutions.