Optical solitons of model with integrable equation for wave packet envelope

Nikolay A. Kudryashov

Chaos, Solitons & Fractals, 2020, vol. 141, issue C

Abstract: We consider the nonlinear fourth-order partial differential equation that can be used for describing solitary waves in nonlinear optics. The Cauchy problem for this equation is not solved by the inverse scattering transform. However we demonstrate that nonlinear ordinary differential equation for description of the wave packet envelope possesses the Painlevé property and is integrable. The Lax pair to this nonlinear ordinary differential equation is presented. Using the determinant for the Lax pair matrix, we find the first integrals of a nonlinear ordinary differential equation. The general solution of the fourth-order nonlinear differential equation is given via the ultraelliptic integrals. Special cases of exact solutions for the fourth-order equation are expressed in terms of the Jacobi elliptic sine. Optical solitons of the original partial differential equation are found.

Keywords: Nonlinear differential equation; Traveling wave; Lax pair; First integral; Solitary wave solution (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307207

DOI: 10.1016/j.chaos.2020.110325

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