Nonautonomous Breather and Rogue Wave in Spinor Bose–Einstein Condensates with Space-Time Modulated Potentials

To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose–Einstein condensates with spatiotemporal modulation,we focus on a system of three coupled Gross–Pitaevskii equations with spacetime-dependent external potentials and temporally modulated gain-loss distributions.With different external potentials and gain-loss distributions,various solutions for controlled nonautonomous matterwave breathers and rogue waves are derived by the Darboux transformation method,such as breathers and rogue waves on arched and constant backgrounds which have the periodic and parabolic trajectories.Effects of the gain-loss distribution and linear potential on the breathers and rogue waves are studied.Nonautonomous two-breathers on the arched and constant backgrounds are also derived.

New solitary waves and exact solutions for the fifth-order nonlinear wave equation using two integration techniques

In this paper,we discussed the enhanced Kudryashov’s and general projective Riccati equations tech-niques for obtaining exact solutions to the fifth-order nonlinear water wave(FONLWWE)equation.Using the enhanced Kudryashov’s method,we were able to achieve solitary wave and singular soliton solutions.Solitary-shock hybrid wave,singular soliton,and periodic wave solutions were discovered when we em-ployed the general projective Riccati equations approach.We can say the given methods are effective and powerful for obtaining exact solutions.Our findings in this paper are critical for explaining a wide range of scientific and oceanographic applications involving ocean gravity waves and other related phenomena.

Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves

In this article,two different methods,namely sub-equation method and residual power series method,have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations,which is a coupled KdV model.The fractional derivative is taken in the conformable sense.Each of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation package.The results indicate that both methods are easy to implement,effective and reliable.They are therefore ready to apply for various partial fractional differential equations.

Generalized solitary wave solutions to the time fractional generalized Hirota-Satsuma coupled KdV via new definition for wave transformation

In this paper,the(G′/G)-expansion method has been applied to explore new solitary wave solutions for the time fractional generalized Hirota-Satsuma coupled KdV(FGHSC KdV)system.The fractional derivative is described with the use of conformable derivative.The results show that this method is a very useful and effective mathematical tool for solving nonlinear conformable fractional equations arising in mathematical physics.As a result,this method can also be applied to other nonlinear conformable fractional differential equations.©2019 Shanghai Jiaotong University.Published by Elsevier B.V.

The Caputo–Fabrizio time-fractional Sharma–Tasso–Olver–Burgers equation and its valid approximations

Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention,in the last decades.The main aim of the current investigation is to consider the time-fractional Sharma–Tasso–Olver–Burgers(STOB)equation in the Caputo–Fabrizio(CF)context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method(HAM)and the Laplace transform.The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition forφ(x,t;u)as the kernel and giving some theorems.To illustrate the CF operator effect on the dynamics of the obtained solitons,several two-and threedimensional plots are formally considered.It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.

Some novel integration techniques to explore the conformable M-fractional Schrödinger-Hirota equation

The current study deals with exact soliton solutions for Schrödinger-Hirota(SH)equation via two modi-fied integration methods.Those methods are known as the improved(G/G)-expansion method and the Kudryashov method.This model is a generalized version of the nonlinear Schrödinger(NLS)equation with higher order dispersion and cubic nonlinearity.It can be considered as a more accurate approximation than the NLS equation in explaining wave propagation in the ocean and optical fibers.A novel deriva-tive operator named as the conformable truncated M-fractional is used to study the above mentioned model.The obtained results can be used in describing the Schrödinger-Hirota equation in some better way.Moreover the obtained results are verified through symbolic computational software.Also,the ob-tained results show that the suggested approaches have broaden capacity to secure some new soliton type solutions for the fractional differential equations in an effective way.In the end,the results are also explained through their graphical representations.