New mapping solutions and localized structures for the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system

Abstract

摘要 映射法是一种非常经典、有效和成熟的求解非线性演化方程的方法，其最大的特点是可以有多种不同形式的设解，使得最终求得的解丰富多彩. 利用改进的 Riccati 方程映射法和变量分离法，得到了(2+1)维非对称 Nizhnik-Novikov-Veselov 系统的新显式精确解.根据得到的孤波解，构造出该系统的峰孤子和分形孤子等局域结构，研究了两个孤立波的“追碰”现象. 关键词: 改进的映射法 / (2+1)维非对称 Nizhnik-Novikov-Veselov 系统 / 局域结构 / “追碰”现象 Abstract The mapping approach is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. Its remarkable characteristic is that we can have infinitely different ansatzs and thus end up with the abundance of solutions. By an improved mapping approach and a variable separation method, a series of excitations of the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system is derived. Based on the derived solitary wave excitation, we obtain some special localized structures such as peakon solitons and fractal solitons, then we discuss the phenomenon of “chase and collision”. Keywords: improved mapping approach / (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system / localized structures / “chase and collision” phenomenon 作者及机构信息 马松华, 方建平, 任清褒 基金项目: 浙江省自然科学基金(批准号：Y604106, Y606128)和丽水学院科研基金(批准号：FC06001, QN06009)资助的课题. Authors and contacts 参考文献 施引文献