Elastic collision of mobile solitons of a (3 + 1)-dimensional soliton equation

• Published in: Nonlinear dynamics Vol. 86; no. 2; pp. 765 - 778
• Main Authors: Darvishi, M. T., Kavitha, L., Najafi, M., Kumar, V. Senthil
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2016; Springer Nature B.V
• Subjects: Algebra; Automotive Engineering; Classical Mechanics; Communications systems; Construction methods; Control; Devices; Dynamical Systems; Elastic scattering; Engineering; Mathematical analysis; Mathematical models; Mechanical Engineering; Nonlinear differential equations; Nonlinear equations; Optical communication; Original Paper; Partial differential equations; Solitary waves; Solitons; Switching; Vibration; Hirota method; Elastic collision; Multi-soliton solution; Soliton equation; Multiple exp-function method; Exact solution
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-016-2920-0

The multiple exp-function method is a new approach to obtain multiple-wave solutions of nonlinear partial differential equations (NLPDEs). By this method, one can obtain multi-soliton solutions of NLPDEs. Hence, in this paper, using symbolic computation, we apply the multiple exp-function method to construct the exact multiple-wave solutions of a (3 + 1)-dimensional soliton equation. Based on this application, we obtain mobile single-wave, double-wave and multi-wave solutions for this equation. In addition, we employ the straightforward and algebraic Hirota bilinearization method to construct the multi-soliton solutions of NLPDEs, and we reveal the remarkable property of soliton–soliton collision through this approach. Further, we investigate the one- and two-soliton solutions of a (3 + 1)-dimensional soliton equation using the Hirota’s method. We explore the particle-like behavior or elastic interaction of solitons, which has potential application in optical communication systems and switching devices.