Novel Soliton Molecules and Wave Interactions for A (3+1)-Dimensional Nonlinear Evolutionary Equation

New wave excitations are revealed for a (3+1)-dimensional nonlinear evolution equation to enrich nonlinear wave patterns in nonlinear systems. Based on a new variable separation solution with two arbitrary variable separated functions obtained by means of the multilinear variable separation approach, localized excitations of N dromions, N x M lump lattice and N x M ring soliton lattice are explored. Interestingly, it is observed that soliton molecules can be composed of diverse "atoms" such as the dromions, lumps and ring solitons, respectively. Elastic interactions between solitons and soliton molecules are graphically demonstrated.

Topological metastability supported by thermal fluctuation upon formation of chiral soliton lattice in $$\hbox {CrNb}_3\hbox {S}_6$$

Topological magnetic structure possesses topological stability characteristics that make it robust against disturbances which are a big advantage for data processing or storage devices of spintronics; nonetheless, such characteristics have been rarely clarified. This paper focused on the formation of chiral soliton lattice (CSL), a one-dimensional topological magnetic structure, and provides a discussion of its topological stability and influence of thermal fluctuation. Herein, CSL responses against change of temperature and applied magnetic field were investigated via small-angle resonant soft X-ray scattering in chromium niobium sulfide ($$\hbox {CrNb}_3\hbox {S}_6$$ CrNb 3 S 6 ). CSL transformation relative to the applied magnetic field demonstrated a clear agreement with the theoretical prediction of the sine-Gordon model. Further, there were apparent differences in the process of chiral soliton creation and annihilation, discussed from the viewpoint of competing between thermal fluctuation and the topological metastability.