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This paper studies a non-compatible fully PT symmetric Davey–Stewartson system which models the evolution of optical wave packet in nonlinear optics. “Non-compatible” means the first two equations of the system are inconsistent that do not need to comply with extra constraint like the compatible case. We employ the multi-linear variable separation approach to derive variable separation solution for this system. The obtained solutions contain four separated free functions, render enough freedom for us to generate diverse solitons. Firstly, we construct two kinds of localized excitations: lump-lattice and periodic-lattice structure. Secondly, we obtain four typical folded solitary waves, i.e. worm-dromion shaped, fin shaped and octopus shaped waves, by introducing suitable multi-valued functions. Lastly, we systematically analyze the interaction between two and three foldons, and give the classification of it. To our knowledge, this is the first time variable separation solution been reported in PT symmetric system. The basic idea of separating variables that used in this paper can be extended to other symmetric systems.

In this work, we employ the multi-linear variable separation approach to derive variable separation solution for a new extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. The solutions obtained here contain two totally separated arbitrary functions without any constraint. In addition, three kinds of localized excitations have been constructed, including dromion-lattice structure, lump-lattice structure and periodic lattice structure. By adjusting the velocities to be equal or unequal, the chase-collision and interaction phenomena have been observed. Moreover, folded solitary waves such as worm shape, worm-dromion shape, worm-solitoff shape, fin shape and octopus shape foldons are derived by introducing multi-valued function. Lastly, we discuss the interaction behavior of two- and three-foldon and construct M × N folded wave. [ABSTRACT FROM AUTHOR]

This paper studies a non-compatible fully P T symmetric Davey–Stewartson system which models the evolution of optical wave packet in nonlinear optics. "Non-compatible" means the first two equations of the system are inconsistent that do not need to comply with extra constraint like the compatible case. We employ the multi-linear variable separation approach to derive variable separation solution for this system. The obtained solutions contain four separated free functions, render enough freedom for us to generate diverse solitons. Firstly, we construct two kinds of localized excitations: lump-lattice and periodic-lattice structure. Secondly, we obtain four typical folded solitary waves, i.e. worm-dromion shaped, fin shaped and octopus shaped waves, by introducing suitable multi-valued functions. Lastly, we systematically analyze the interaction between two and three foldons, and give the classification of it. To our knowledge, this is the first time variable separation solution been reported in P T symmetric system. The basic idea of separating variables that used in this paper can be extended to other symmetric systems. • This paper studies a non-compatible fully P T symmetric Davey–Stewartson system. • The obtained solutions contain four separated free functions. • Diverse localized excitation and folded solitary waves are obtained. [ABSTRACT FROM AUTHOR]