https://doi.org/10.1140/epjp/i2018-12354-9
Regular Article
More general families of exact solitary wave solutions of the nonlinear Schrödinger equation with their applications in nonlinear optics
1
Department of Mathematics, Harbin Institute of Technology, 150001, Harbin, China
2
Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
3
Mathematics Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt
* e-mail: Aly742001@yahoo.com
Received:
13
October
2018
Accepted:
1
November
2018
Published online:
24
December
2018
In this article we analytically studied the complex nonlinear Schrödinger equation with Kerr law nonlinearity using the auxiliary equation mapping method, as a result, we found a series of more general and new families of exact solutions, which are more powerful in the development of soliton dynamics, quantum plasma, adiabatic parameter dynamics, biomedical problems, fluid dynamics, industrial studies, nonlinear optics and many other fields. The calculations demonstrate that this method is more reliable, straightforward and effective to analytically study other nonlinear complicated physical problems modeled by complex nonlinear partial differential equations arising in mathematical physics, hydrodynamics, fluid mechanics, mathematical biology, plasma physics, engineering disciplines, chemistry and many other natural sciences. We have also expressed our solutions graphically with the help of Mathematica 10.4 to physically understand the behavior of different shapes of solutions including kink-type, anti-kink-type, half-bright and dark solitons.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018