Search

This work investigates the nonlinear Rangwala–Rao equation, which stems from the mixed derivative nonlinear Schrödinger equation. For retrieving new exact solutions to the equation, the complete discriminant system for polynomial method is employed. In results, some novel traveling wave solutions, including solitary wave solutions, triangular function solutions, periodic solutions and Jacobi elliptic function solutions are obtained and demonstrated through numerical simulations. The bifurcations of phase velocity fields are depicted to reveal the dynamic behavior of the Rangwala-Rao equation using the qualitative theory of dynamical systems. Furthermore, considering external perturbation, the chaotic motions of the perturbed Rangwala-Rao equation are investigated.

In this paper, the stochastic space-fractional long-short-wave interaction system (SF-LSWIS) with multiplicative white noise is considered. The stochastic exact solutions, including triangular function solutions, hyperbolic function solutions, and Jacobi elliptic function solutions, are obtained via the complete discriminant system for polynomial method. For this purpose, the traveling wave transformation is applied to carry out the ordinary differential equation of this model, which is also converted to a dynamical system. Thereafter, qualitative behavior and bifurcation of the phase portraits of the dynamical system are investigated using the qualitative theory of dynamical systems. The chaotic behaviors of the system considering external periodic perturbation are studied. Furthermore, the 3D surface, graphs of contour plots, and level curves of some exact solutions are depicted by choosing proper parameter values. The influence and effect of fractional derivatives and noise strength on the solutions are also studied.

This work investigates the nonlinear Rangwala–Rao equation, which stems from the mixed derivative nonlinear Schrödinger equation. For retrieving new exact solutions to the equation, the complete discriminant system for polynomial method is employed. In results, some novel traveling wave solutions, including solitary wave solutions, triangular function solutions, periodic solutions and Jacobi elliptic function solutions are obtained and demonstrated through numerical simulations. The bifurcations of phase velocity fields are depicted to reveal the dynamic behavior of the Rangwala-Rao equation using the qualitative theory of dynamical systems. Furthermore, considering external perturbation, the chaotic motions of the perturbed Rangwala-Rao equation are investigated. • This paper studies the nonlinear Rangwala–Rao equation. • The exact solutions of this mode are obtained using the trial equation method. • Bifurcation, phase portrait, sensitivity analysis, and chaotic behavior of the equation are obtained. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic space-fractional long-short-wave interaction system (SF-LSWIS) with multiplicative white noise is considered. The stochastic exact solutions, including triangular function solutions, hyperbolic function solutions, and Jacobi elliptic function solutions, are obtained via the complete discriminant system for polynomial method. For this purpose, the traveling wave transformation is applied to carry out the ordinary differential equation of this model, which is also converted to a dynamical system. Thereafter, qualitative behavior and bifurcation of the phase portraits of the dynamical system are investigated using the qualitative theory of dynamical systems. The chaotic behaviors of the system considering external periodic perturbation are studied. Furthermore, the 3D surface, graphs of contour plots, and level curves of some exact solutions are depicted by choosing proper parameter values. The influence and effect of fractional derivatives and noise strength on the solutions are also studied. • The stochastic space-fractional long-short-wave interaction system is studied. • The exact solutions to this model are obtained using the complete discrimination system for polynomial method. • Phase portrait, bifurcation, and chaotic pattern of the equation are studied. [ABSTRACT FROM AUTHOR]