Preprint Article Version 1 This version is not peer-reviewed

Bright and Singular Soliton Solutions of Tzitzéica Type Equations Appear in Nonlinear Optics

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. Preprints 2019, 2019010063 (doi: 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 (doi: 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.

Subject Areas

Tzitzéica-Dodd–Bullough–Mikhailov equation; Tzitzéica-type equation; ansatz approach; traveling wave solution; periodic solutions

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