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With the help of the Maple symbolic computation system and the projective equation approach, a new family of variable separation solutions with arbitrary functions for the (2+1)-dimensional generalized Breor-Kaup (GBK) system is derived. Based on the derived solitary wave solution, some chaotic behaviors of the GBK system are investigated. [ABSTRACT FROM AUTHOR]

In this paper, by means of similarity transfomations, we obtain explicit solutions to the cubic-quintic nonlinear Schrödinger equation with varying coefficients, which involve four free functions of space. Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations. [ABSTRACT FROM AUTHOR]

Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for a general (2+1)-dimensional Korteweg de Vries system (GKdV) is derived. According to the derived solutions, we obtain some novel dromion-lattice solitons, complex wave excitations and chaotic patterns for the GKdV system. [ABSTRACT FROM AUTHOR]

By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Boiti--Leon--Pempinelli (BLP) system is derived. Based on the derived solitary wave solution, some dromion and solitoff excitations and chaotic behaviours are investigated. [ABSTRACT FROM AUTHOR]

By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated. [ABSTRACT FROM AUTHOR]