Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method

• Published in: Optical and quantum electronics Vol. 51; no. 7; pp. 1 - 36
• Main Authors: Kumar, Dipankar, Joardar, Atish Kumar, Hoque, Ashabul, Paul, Gour Chandra
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-07-2019; Springer Nature B.V
• Subjects: Brightening; Characterization and Evaluation of Materials; Computation; Computer Communication Networks; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; DIAGRAMS; DIPOLES; Electrical Engineering; GRAPH THEORY; Graphs; Hyperbolic functions; Lasers; LIQUID CRYSTALS; NONLINEAR PROBLEMS; Optical Devices; Optics; PERIODICITY; Photonics; Physics; Physics and Astronomy; Solitary waves; SOLITONS; Trigonometric functions; Kerr law; The extended sinh-Gordon equation expansion method; Parabolic law; Nematicons; Solitons
• ISSN: 0306-8919; 1572-817X
• DOI: 10.1007/s11082-019-1917-6

This paper secures new nematicons in liquid crystals from its governing equation by extended sinh-Gordon equation expansion method with the aid of symbolic computational package Maple. The two laws of nonlinearity, namely Kerr and parabolic laws are studied. As outcomes, some new explicit complex hyperbolic and complex trigonometric function solutions are derived regarding dark, bright, combined dark–bright, singular, combined singular optical, periodic wave, dipole soliton solutions and others. To show the real physical meaning of the derived results, three dimensional graphs with contours and two dimensional graphs are prepared under the choice of proper values of the arbitrary parameters. The derived solutions have been checked back into their corresponding equations with the symbolic computational package Maple. All the combined solutions are found to be new, which may play an important role in the context of liquid crystals. The applied method is found to provide a powerful tool for extracting exact solitary wave solutions and overcome the difficulties of the solitary wave ansatz method.