Conservation laws and Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients in nonlinear optics

• Published in: Nonlinear dynamics Vol. 77; no. 4; pp. 1331 - 1337
• Main Authors: Qi, Feng-Hua, Ju, Hong-Mei, Meng, Xiang-Hua, Li, Juan
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2014; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Conservation laws; Control; Dynamical Systems; Energy conservation; Engineering; Mechanical Engineering; Nonlinear equations; Nonlinear optics; Nonlinearity; Optical fibers; Original Paper; Pulse propagation; Schrodinger equation; Solitary waves; Transformations; Vibration; Waveguides; Conservation laws; Coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients; Symbolic computation; Darboux transformation
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-014-1382-5

In this paper, by Darboux transformation and symbolic computation we investigate the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the non-Kerr media. Lax pair of the equations is obtained, and the corresponding Darboux transformation is constructed. One-soliton solutions are derived; some physical quantities such as the amplitude, velocity, width, initial phases, and energy are, respectively, analyzed; and finally an infinite number of conservation laws are also derived. These results might be of some value for the ultrashort optical pulse propagation in the non-Kerr media.