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

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Abstract

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.

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Acknowledgments

The author L.K. gratefully acknowledges the financial support from UGC, India in the form of a Research Award, NBHM, India in the form of a Major Research Project, DAE-BRNS, India in the form of a Young Scientist Research Award and ICTP, Italy in the form of a Regular Associateship.

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Authors and Affiliations

  1. Department of Mathematics, Razi University, Kermanshah, 67149, Iran

    M. T. Darvishi & M. Najafi

  2. Department of Physics, School of Basic and Applied Sciences, Central University of Tamilnadu (CUTN), Thiruvarur, Tamilnadu, 610 101, India

    L. Kavitha

  3. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

    L. Kavitha

  4. Department of Physics, Periyar University, Salem, Tamilnadu, 636 011, India

    V. Senthil Kumar

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  1. M. T. Darvishi
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Correspondence to L. Kavitha.

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Darvishi, M.T., Kavitha, L., Najafi, M. et al. Elastic collision of mobile solitons of a (3 + 1)-dimensional soliton equation. Nonlinear Dyn 86, 765–778 (2016). https://doi.org/10.1007/s11071-016-2920-0

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