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

Asim Zafar; Alper Korkmaz; Muhammad Imran Qureshi; Asfand Fahad

doi:10.20944/preprints201901.0063.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 5 January 2019 / Approved: 8 January 2019 / Online: 8 January 2019 (11:16:12 CET)

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.

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

Computer Science and Mathematics, Applied Mathematics

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

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