Operational systems of spacecraft are general variable mass mechanics systems, and their symmetries and conserved quantities imply profound physical rules of the space system. We study the Mei symmetry of Tzénoff equations for a variable mass nonholonomic system and the new conserved quantities derived. The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented. This result has some theoretical values in further research of conservation laws obeyed by the variable mass system.

Based upon the group theoretical jet bundle formalism introduced by Wahlquist and Estabrook for discussing the complete integrability of soliton systems, we investigate the prolongation structure of Wadati—Konno—Ichikawa isospectral evolution equations. As a result, we unearth a new physical coupled system entailing a hidden structural symmetry SL(3, R) arising in the description of ultra-short pulse propagation in optical nonlinear media. As a matter of fact, we depict a graphical representation of one-breather and two-breather ultra-short pulses in motion with a non-zero angular momentum. By extending the previous study to multidimensional symmetry SL(n, R), we unearth a more general class of multicomponent coupled nonlinear ultra-short pulse system with its associated inverse scattering formulation particularly useful in soliton theory.

Two classes of periodic wave solutions to the (3+1)-dimensional soliton equation are derived by employing the Hirota bilinear method and theta function identities. These solutions are expressed in terms of Riemann theta functions of genus one and can be converted into an elliptic function format, both their long wave limit and extremum value are discussed in detail.

The anisotropy of dipole-dipole interaction is revealed by energy band, tunneling dynamics and stabilities of a dipolar condensate in one-dimensional optical lattices. It is demonstrated that the Bloch band structure, the tunneling rate between Bloch bands and the stabilities of Bloch states can be controlled by adjusting the effective aspect ratio of the condensate and the dipolar orientation.

The decoherence effect on multipartite entanglement in non-inertial frames is investigated. The GHZ state is considered to be shared between partners with one partner in the inertial frame whereas the other two are in accelerated frames. One-tangle and π-tangles are used to quantify the entanglement of the multipartite system influenced by phase damping and phase flip channels. It is seen that for the phase damping channel, entanglement sudden death (ESD) occurs for p > 0.5 in the infinite acceleration limit. On the other hand, in the case of the phase flip channel, ESD behavior occurs at p = 0.5. It is also seen that entanglement sudden birth (ESB) occurs in the case of phase flip channel just after ESD, i.e. p > 0.5. Furthermore, it is seen that the effect of the environment on multipartite entanglement is much stronger than that of the acceleration of non-inertial frames.

The Schrödinger equation for the generalized Pöschl—Teller potential with the centrifugal term is investigated approximately. The Nikiforov—Uvarov method is used in the calculations and the eigenfunctions as well as the energy eigenvalues obtained after a proper Pekeris-type approximation. Some useful expectation values and the oscillator strength are reported.

We revisit Parikh—Wilczek tunneling through the de Sitter horizon and obtain the tunneling rate in Schwarzschild-de Sitter space, which is non-thermal and closely related to the change of entropy. We discuss the thermodynamics of Schwarzschild-de Sitter space and show existence of correlation which can ensure conservation of the total entropy in the transition process of Schwarzschild-de Sitter space to de Sitter space. The correlation and the conserved entropy provide a way to explain the entropy in empty de Sitter space.

We carry out the hidden structural symmetries embedded within a system comprising ultra-short pulses which propagate in optical nonlinear media. Based upon the Wahlquist-Estabrook approach, we construct the Lie-algebra valued connections associated to the previous symmetries while deriving their corresponding Lax-pairs, which are particularly useful in soliton theory. In the wake of previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2+1)-dimensional ultra-short pulse equation is unveiled along with its inverse scattering formulation, the application of which are straightforward in nonlinear optics where an additional propagating dimension deserves some attention.

Time-delay Takagi-Sugeno fuzzy drive-response dynamical networks (TD-TSFDRDNs) are defined by extending the drive-response dynamical networks. Based on the LaSalle invariant principle, a simple and systematic adaptive control scheme is proposed to synchronize the TD-TSFDRDNs with a desired scalar factor. A sufficient condition for the generalized projective synchronization in TD-TSFDRDNs is derived. Moreover, numerical simulations are provided to verify the correctness and effectiveness of the scheme.

We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies. Based on graph theory and Lyapunov stability theory, the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations. Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.