New Type Of Variable Separation Solution Research Articles

Diversity soliton excitations for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation

With the aid of symbolic computation, we derive new types of variable separation solutions for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation based on an improved mapping approach. Rich coherent structures like the soliton-type, rouge wave-type, and cross-like fractal type structures are presented, and moreover, the fusion interactions of localized structures are graphically investigated. Some of these solutions exhibit a rich dynamic, with a wide variety of qualitative behavior and structures that are exponentially localized.

Localized Excitations of (2+1)-Dimensional Korteweg-deVries System Derived from a Periodic WaveSolution

With the aid of an improved projective approach and a linearvariable separation method, new types of variable separationsolutions (including solitary wave solutions, periodic wavesolutions, and rational function solutions) with arbitraryfunctions for (2+1)-dimensional Korteweg-de Vries system arederived. Usually, in terms of solitary wave solutions and rationalfunction solutions, one can find some important localizedexcitations. However, based on the derived periodic wave solutionin this paper, we find that some novel and significant localizedcoherent excitations such as dromions, peakons, stochasticfractal patterns, regular fractal patterns, chaotic line solitonpatterns as well as chaotic patterns exist in the KdV system asconsidering appropriate boundary conditions and/or initial qualifications.

New Family of Exact Solutions and Chaotic Soltions of Generalized Breor–KaupSystem in (2+1)-Dimensions via an Extended Mapping Approach**The projectsupported by the Natural Science Foundation of Zhejiang Province under GrantNo. Y604106, the Foundation of New Century ``151 Talent Engineering''of Zhejiang Province, the Scientific Research Foundation of KeyDiscipline of Zhejiang Province, and the Natural ScienceFoundation of Zhejiang Lishui University under Grant No.

Starting from an extended mapping approach, a new type of variableseparation solution with arbitrary functions of generalized(2+1)-dimensional Broer–Kaup system (GBK) system is derived. Thenbased on the derived solitary wave solution, we obtain some specificchaotic solitons to the (2+1)-dimensional GBK system.

Variable Separation Solutions of Generalized Broer–Kaup Systemvia a Projective Method

Using an extended projective method, a new type of variableseparation solution with two arbitrary functions of the(2+1)-dimensional generalized Broer-Kaup system (GBK) is derived.Based on the derived variable separation solution, some speciallocalized coherent soliton excitations with or without elasticbehaviors such as dromions, peakons, and foldons etc. arerevealed by selecting appropriate functions in this paper.