中国物理B ›› 2017, Vol. 26 ›› Issue (7): 70201-070201.doi: 10.1088/1674-1056/26/7/070201

• GENERAL •    下一篇

Multiple exp-function method for soliton solutions ofnonlinear evolution equations

Yakup Yıldırım, Emrullah Yašar   

  1. Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, Turkey
  • 收稿日期:2017-03-06 修回日期:2017-03-23 出版日期:2017-07-05 发布日期:2017-07-05
  • 通讯作者: Emrullah Yašar E-mail:eyasar@uludag.edu.tr

Multiple exp-function method for soliton solutions ofnonlinear evolution equations

Yakup Y?ld?r?m, Emrullah Yašar   

  1. Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, Turkey
  • Received:2017-03-06 Revised:2017-03-23 Online:2017-07-05 Published:2017-07-05
  • Contact: Emrullah Yašar E-mail:eyasar@uludag.edu.tr

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摘要：

We applied the multiple exp-function scheme to the (2+1)-dimensional Sawada–Kotera (SK) equation and (3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.

关键词: (2+1)-dimensional Sawada–, Kotera (SK) equation, (3+1)-dimensional nonlinear evolution equation (NLEE), multiple exp-function method, multiple wave solutions

Abstract:

We applied the multiple exp-function scheme to the (2+1)-dimensional Sawada–Kotera (SK) equation and (3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.

Key words: (2+1)-dimensional Sawada–, Kotera (SK) equation, (3+1)-dimensional nonlinear evolution equation (NLEE), multiple exp-function method, multiple wave solutions

中图分类号:  (Special functions)

  • 02.30.Gp
02.30.Ik (Integrable systems) 02.30.Jr (Partial differential equations)