Search

This paper constructs dark, bright, combined dark-bright, singular, combined singular soliton optical and singular periodic solutions to the conformable space-time fractional second order nonlinear Schrödinger equation with group velocity dispersion coefficient and spatiotemporal dispersion by using the extended sinh-Gordon equation expansion method. The constraint conditions for the existence of valid soliton solutions are given. The reported results in this study may be helpful in explaining the physical meaning of the studied model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate and use the new modified exp ( − Ω ( ξ ) ) -expansion method, (MEM). We apply the new MEM to nonlinear long–short-wave interaction systems (NLSWIS). Among our findings are sets of solutions including, but not limited to, new hyperbolic, complex, and dark soliton solutions. Not only is MEM shown to be highly adaptable for partial differential equations with strong nonlinearities, but also, it turns out to be highly efficient, despite its ease. [ABSTRACT FROM AUTHOR]

In this study, we apply the modified exp ( - Ω ( ξ ) ) - expansion function method to the new coupled Konno-Oono equation. We obtain some new travelling wave solutions such as complex function, hyperbolic function and rational function solutions. We observe that all travelling wave solutions have been verified the new coupled Konno-Oono equation by using Wolfram Mathematica 9. Then, we plot the two- and three-dimensional surfaces for all travelling wave solutions obtained in this paper by the same computer program. [ABSTRACT FROM AUTHOR]

In this paper, we apply auto-Bäcklund transformation for Sharma-Tasso-Olver (STO) equation and fourth order equation of the Burgers hierarchy. Auto-Bäcklund transformation was developed as a direct and simple method to obtain solutions of nonlinear partial differential equations by Fan.We obtain solitary wave solutions of these equations.The numerical simulations are added to these obtained solutions [ABSTRACT FROM AUTHOR]