Abundant soliton structures of \((2+1)\)-dimensional NLS equation.
Using the variable separation approach for the \((2+1)\)-dimensional NLS equation, the authors obtain some new types of multi-soliton solutions because of the existence of arbitrary functions appearing in seed solution. By selecting the arbitrary functions appropriately, the multiple localized solutions may be dromions, breathers, instantons, etc. The dromions may be driven. \((2+1)\)-dimensional breathers may breath not only in its amplitudes but also in its shapes. The instantons in \((2+1)\) dimensions may have also quite rich structures. The authors hope that the method developed in this paper may also be used to other \((2+1)\)-dimensional integrable models.
scientific article; zbMATH DE number 2027071