A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced(3+1)-Dimensional Nonlinear Evolution Equation

With symbolic computation, some lump solutions are presented to a(3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters.

Stable stripe and vortex solitons in two-dimensional spin-orbit coupled Bose-Einstein condensates

We present a flexible manipulation and control of solitons via Bose-Einstein condensates.In the presence of Rashba spin-orbit coupling and repulsive interactions within a harmonic potential,our investigation reveals the numerical local solutions within the system.By manipulating the strength of repulsive interactions and adjusting spin-orbit coupling while maintaining a zero-frequency rotation,diverse soliton structures emerge within the system.These include plane-wave solitons,two distinct types of stripe solitons,and odd petal solitons with both single and double layers.The stability of these solitons is intricately dependent on the varying strength of spin-orbit coupling.Specifically,stripe solitons can maintain a stable existence within regions characterized by enhanced spin-orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions.When rotational frequency is introduced to the system,solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation.The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin-orbit coupling.As a result,the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.