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With the help of the conditional similarity reduction method, a new family of complex wave solutions with q= lx + my + kt + Γ( x, y, t) for the (2+1)-dimensional modified dispersive water-wave (MDWW) system are obtained. Based on the derived solitary wave solution, some novel complex wave localised excitations are investigated. [ABSTRACT FROM AUTHOR]

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]

In this paper, an objective reduction approach (a special conditional reduction approach) is presented. As a concrete application in nonlinear physical system, new types of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for the (2+1)-dimensional modified dispersive long-wave system are derived via the objective reduction approach. As special reduction cases based on the derived variable separation solutions, it is shown that some localized coherent structures like nonpropagating and propagating solitons with physical meaning exist in the (2+1)-dimensional modified dispersive long-wave system by prescribing different values of the arbitrary parameters in this short note. [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]