Novel solitary wave solution of the nonlinear fractal Schrodinger equation and its fractal variational principle

摘要

Purpose - The nonlinear Schrodinger equation plays a vital role in wave mechanics and nonlinear optics. The purpose of this paper is the fractal paradigm of the nonlinear Schrodinger equation for the calculation of novel solitary solutions through the variational principle. Design/methodology/approach - Appropriate traveling wave transform is used to convert a partial differential equation into a dimensionless nonlinear ordinary differential equation that is handled by a semi-inverse variational technique. Findings - This paper sets out the Schrodinger equation fractal model and its variational principle. The results of the solitary solutions have shown that the proposed approach is very accurate and effective and is almost suitable for use in such problems. Practical implications - Nonlinear Schrodinger equation is an important application of a variety of various situations in nonlinear science and physics, such as photonics, the theory of superfluidity, quantum gravity, quantum mechanics, plasma physics, neutron diffraction, nonlinear optics, fiber-optic communication, capillary fluids, Bose-Einstein condensation, magma transport and open quantum systems. Originality/value - The variational principle of the Schrodinger equation without the Lagrange multiplier method in the sense of the fractal calculus is developed for the first time in the literature to the best of the author's understanding.