Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained...Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.展开更多
With the aid of an improved projective approach and a linear variable separation method, new types of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function s...With the aid of an improved projective approach and a linear variable separation method, new types of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （2＋1）-dimensional Korteweg-de Vries system are derived. Usually, in terms of solitary wave solutions and rational function solutions, one can find some important localized excitations. However, based on the derived periodic wave solution in this paper, we find that some novel and significant localized coherent excitations such as dromions, peakons, stochastic fractal patterns, regular fractal patterns, chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.展开更多
Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the （3＋1）-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functi...Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the （3＋1）-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures （new dromions） are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures （dromions） are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic.展开更多
Extended mapping approach is introduced to solve （2＋1）-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excit...Extended mapping approach is introduced to solve （2＋1）-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.展开更多
We investigate the nonlinear localized structures of optical pulses propagating in a one-dimensional photonic crystal with a quadratic nonlinearity. Using a method of multiple scales we show that the nonlinear evolut...We investigate the nonlinear localized structures of optical pulses propagating in a one-dimensional photonic crystal with a quadratic nonlinearity. Using a method of multiple scales we show that the nonlinear evolution of a wave packet, formed by the superposition of short-wavelength excitations, and long-wavelength mean fields, generated by the self-interaction of the wave packet, are governed by a set of coupled high-dimenslonal nonlinear envelope equations, which can be reduced to Davey-Stewartson equations and thus support dromionlike high-dimensional nonlinear excitations in the system.展开更多
文摘Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05005 The authors are in debt to Profs. J.P. Fang, C.Z. Xu, and J.F. Zhang, and Drs. H.P. Zhu, Z.Y. Ma, and W.H. Huang for their fruitful discussions.
文摘With the aid of an improved projective approach and a linear variable separation method, new types of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （2＋1）-dimensional Korteweg-de Vries system are derived. Usually, in terms of solitary wave solutions and rational function solutions, one can find some important localized excitations. However, based on the derived periodic wave solution in this paper, we find that some novel and significant localized coherent excitations such as dromions, peakons, stochastic fractal patterns, regular fractal patterns, chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.
基金The project supported by National Natural Science Foundation of China under Grant No. 10575082
文摘Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the （3＋1）-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures （new dromions） are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures （dromions） are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic.
基金The authors would like to thank Profs. Jie-Fang Zhang and Chun-Long Zheng for helpful discussions.
文摘Extended mapping approach is introduced to solve （2＋1）-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 90403008 and 10434060, and the State Key Major Research and Development Program of China
文摘We investigate the nonlinear localized structures of optical pulses propagating in a one-dimensional photonic crystal with a quadratic nonlinearity. Using a method of multiple scales we show that the nonlinear evolution of a wave packet, formed by the superposition of short-wavelength excitations, and long-wavelength mean fields, generated by the self-interaction of the wave packet, are governed by a set of coupled high-dimenslonal nonlinear envelope equations, which can be reduced to Davey-Stewartson equations and thus support dromionlike high-dimensional nonlinear excitations in the system.
