Version 1
: Received: 5 January 2019 / Approved: 8 January 2019 / Online: 8 January 2019 (11:16:12 CET)
How to cite:
Zafar, A.; Korkmaz, A.; Qureshi, M. I.; Fahad, A. Bright and Singular Soliton Solutions of Tzitzéica Type Equations Appear in Nonlinear Optics. Preprints2019, 2019010063. https://doi.org/10.20944/preprints201901.0063.v1
Zafar, A.; Korkmaz, A.; Qureshi, M. I.; Fahad, A. Bright and Singular Soliton Solutions of Tzitzéica Type Equations Appear in Nonlinear Optics. Preprints 2019, 2019010063. https://doi.org/10.20944/preprints201901.0063.v1
Zafar, A.; Korkmaz, A.; Qureshi, M. I.; Fahad, A. Bright and Singular Soliton Solutions of Tzitzéica Type Equations Appear in Nonlinear Optics. Preprints2019, 2019010063. https://doi.org/10.20944/preprints201901.0063.v1
APA Style
Zafar, A., Korkmaz, A., Qureshi, M. I., & Fahad, A. (2019). Bright and Singular Soliton Solutions of Tzitzéica Type Equations Appear in Nonlinear Optics. Preprints. https://doi.org/10.20944/preprints201901.0063.v1
Chicago/Turabian Style
Zafar, A., Muhammad Imran Qureshi and Asfand Fahad. 2019 "Bright and Singular Soliton Solutions of Tzitzéica Type Equations Appear in Nonlinear Optics" Preprints. https://doi.org/10.20944/preprints201901.0063.v1
Abstract
We investigate the exact travelling wave solutions of the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations, appear in nonlinear optics, using simple ansatz approach. We use the Painlevé and traveling wave transformations to convert the mentioned nonlinear equations into nonlinear ordinary differential equations. Then, the simple ansatz approach has been employed to procure wave solutions, in terms of bright, singular soliton and trigonometric functions, for the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations. The study shows that the simple ansatz approach is straightforward and easy to implement for solving nonlinear problems.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.