New variable separation solutions and localized waves for (2+1)-dimensional nonlinear systems by a full variable separation approach

被引:6
作者
Quan, Jingfeng
Tang, Xiaoyan [1 ]
机构
[1] East China Normal Univ, Sch Math Sci, Key Lab Math & Engn Applicat, Minist Educ, Shanghai 200241, Peoples R China
基金
中国国家自然科学基金;
关键词
full variable separation approach; full variable separation solution; localized waves; on-site interaction; DROMION SOLUTIONS; SIMILARITY REDUCTIONS; COHERENT STRUCTURES; SPECTRAL TRANSFORM; INVERSE SCATTERING; EQUATION; SOLITON;
D O I
10.1088/1402-4896/ad0e4d
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A full variable separation approach is firstly proposed for (2+1)-dimensional nonlinear systems by extending the well-established multilinear variable separation approach through the assumption that the expansion function is composed of full variable separated functions, namely, functions with respect to only one spacial or temporal argument. Taking the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation, the Nizhnik-Novikov-Veselov equation and the dispersive long wave equation as examples, new full variable separation solutions are obtained with several arbitrary one dimensional functions. Especially, a common formula for some suitable physical quantities is discovered. By taking the arbitrary functions in different explicit expressions, the solutions can be used to describe plentiful novel nonlinear localized waves, which might be non-travelling waves as the spacial and temporal variables are fully separated into different functions. In particular, some new hybrid solitary waves, which can pulsate periodically, appear and/or decay with an adjustable lifetime, are discovered through the on-site interactions between a doubly periodic wave and a ring soliton, a four-humped dromion and a four-humped lump, and a doubly periodic wave and a cross type solitary wave. Nonlinear wave structures and their dynamical behaviours are discussed and graphically displayed in detail.
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页数:21
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