The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation

doi:10.1088/1674-1056/ad9912

中国物理B ›› 2025, Vol. 34 ›› Issue (2): 20502-020502.doi: 10.1088/1674-1056/ad9912

The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation

Pengcheng Xin(辛鹏程), Zhonglong Zhao(赵忠龙)†, and Yu Wang(王宇)

School of Mathematics, North University of China, Taiyuan 030051, China

收稿日期:2024-10-24 修回日期:2024-11-28 接受日期:2024-12-02 出版日期:2025-02-15 发布日期:2025-01-15
通讯作者: Zhonglong Zhao E-mail:zhaozlhit@163.com,zhaozl@nuc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12101572 and 12371256), 2024 Shanxi Province Graduate Innovation Project (Grant No. 2024KY615), and the Fundamental Research Program of Shanxi Province of China (Grant No. 202403021211002).

The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation

Pengcheng Xin(辛鹏程), Zhonglong Zhao(赵忠龙)†, and Yu Wang(王宇)

School of Mathematics, North University of China, Taiyuan 030051, China

Received:2024-10-24 Revised:2024-11-28 Accepted:2024-12-02 Online:2025-02-15 Published:2025-01-15
Contact: Zhonglong Zhao E-mail:zhaozlhit@163.com,zhaozl@nuc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12101572 and 12371256), 2024 Shanxi Province Graduate Innovation Project (Grant No. 2024KY615), and the Fundamental Research Program of Shanxi Province of China (Grant No. 202403021211002).

摘要/Abstract

摘要： The $N$-periodic wave solvability problem for the ${\cal N} =1$ supersymmetric Sawada-Kotera-Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the $N$-periodic wave solutions is derived. It has been verified that under certain conditions, the asymptotic relations between $N$-periodic wave solutions and $N$-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.

关键词: supersymmetry, $N$-periodic wave solutions, asymptotic relations

Abstract: The $N$-periodic wave solvability problem for the ${\cal N} =1$ supersymmetric Sawada-Kotera-Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the $N$-periodic wave solutions is derived. It has been verified that under certain conditions, the asymptotic relations between $N$-periodic wave solutions and $N$-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.

Key words: supersymmetry, $N$-periodic wave solutions, asymptotic relations

中图分类号: (Solitons)

05.45.Yv

42.65.Tg (Optical solitons; nonlinear guided waves) 03.65.Ge (Solutions of wave equations: bound states)

Pengcheng Xin(辛鹏程), Zhonglong Zhao(赵忠龙), and Yu Wang(王宇). The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation[J]. 中国物理B, 2025, 34(2): 20502-020502.

Pengcheng Xin(辛鹏程), Zhonglong Zhao(赵忠龙), and Yu Wang(王宇). The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation[J]. Chin. Phys. B, 2025, 34(2): 20502-020502.

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The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation

The N-periodic wave solutions to the N =1 supersymmetric Sawada-Kotera-Ramani equation

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