We present new lemmas,theorem and corollaries to construct interactions among higher-order rogue waves,n-periodic waves and n-solitons solutions(n→∞)to the(2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov(ANNV)eq...We present new lemmas,theorem and corollaries to construct interactions among higher-order rogue waves,n-periodic waves and n-solitons solutions(n→∞)to the(2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov(ANNV)equation.Several examples for theories are given by choosing definite interactions of the wave solutions for the model.In particular,we exhibit dynamical interactions between a rogue and a cross bright-dark bell wave,a rogue and a cross-bright bell wave,a rogue and a one-,two-,three-,four-periodic wave.In addition,we also present multi-types interactions between a rogue and a periodic cross-bright bell wave,a rogue and a periodic cross-bright-bark bell wave.Finally,we physically explain such interaction solutions of the model in the 3D and density plots.展开更多
In this paper,the direct symmetry method is extended to the Lax pair of the ANNV equation.As a result,symmetries of the Lax pair and the ANNV equation are obtained at the same time.Applying the obtained symmetry,the (...In this paper,the direct symmetry method is extended to the Lax pair of the ANNV equation.As a result,symmetries of the Lax pair and the ANNV equation are obtained at the same time.Applying the obtained symmetry,the (2+1)-dimensionai Lax pair is reduced to (1+1)-dimensional Lax pair,whose compatibility yields the reduction ofthe ANNV equation.Based on the obtained reductions of the ANNV equation,a lot of new exact solutions for theANNV equation are found.This shows that for an integrable system,both the symmetry and the reductions can beobtained through its corresponding Lax pair.展开更多
Starting from the extended tanh-function method （ETM） based on the mapping method, the variable separation solutions of the （2＋1）-dimensional asymmetric Nizhnik Novikov Veselov （ANNV） system are derived. By fur...Starting from the extended tanh-function method （ETM） based on the mapping method, the variable separation solutions of the （2＋1）-dimensional asymmetric Nizhnik Novikov Veselov （ANNV） system are derived. By further study, we find that these variable separation solutions are seemingly independent of but actually dependent on each other. Based on the variable separation solution and by choosing appropriate functions, some novel and interesting interactions between special solitons, such as bell-like compacton, peakon-like compacton and compacton-like semifoldon, are investigated.展开更多
This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨...This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨ cklund transformation was first obtained, and then the richness of the localized coherent structures was found, which was caused by the entrance of two variable separated arbitrary functions, in the model. For some special choices of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, and ring solitons.展开更多
A new(2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov(eANNV)equation is proposed by introducing the additional bilinear terms to the usual ANNV equation.Based on the independent transformatio...A new(2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov(eANNV)equation is proposed by introducing the additional bilinear terms to the usual ANNV equation.Based on the independent transformation,the bilinear form of the eANNV equation is constructed.The lump wave is guaranteed by introducing a positive constant term in the quadratic function.Meanwhile,different class solutions of the eANNV equation are obtained by mixing the quadratic function with the exponential functions.For the interaction between the lump wave and one-soliton,the energy of the lump wave and one-soliton can transfer to each other at different times.The interaction between a lump and two-soliton can be obtained only by eliminating the sixth-order bilinear term.The dynamics of these solutions are illustrated by selecting the specific parameters in three-dimensional,contour and density plots.展开更多
文摘We present new lemmas,theorem and corollaries to construct interactions among higher-order rogue waves,n-periodic waves and n-solitons solutions(n→∞)to the(2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov(ANNV)equation.Several examples for theories are given by choosing definite interactions of the wave solutions for the model.In particular,we exhibit dynamical interactions between a rogue and a cross bright-dark bell wave,a rogue and a cross-bright bell wave,a rogue and a one-,two-,three-,four-periodic wave.In addition,we also present multi-types interactions between a rogue and a periodic cross-bright bell wave,a rogue and a periodic cross-bright-bark bell wave.Finally,we physically explain such interaction solutions of the model in the 3D and density plots.
基金Natural Science Foundation of Shandong Province under Grant Nos.2004zx16 and Q2005A01
文摘In this paper,the direct symmetry method is extended to the Lax pair of the ANNV equation.As a result,symmetries of the Lax pair and the ANNV equation are obtained at the same time.Applying the obtained symmetry,the (2+1)-dimensionai Lax pair is reduced to (1+1)-dimensional Lax pair,whose compatibility yields the reduction ofthe ANNV equation.Based on the obtained reductions of the ANNV equation,a lot of new exact solutions for theANNV equation are found.This shows that for an integrable system,both the symmetry and the reductions can beobtained through its corresponding Lax pair.
基金Project supported by the National Natural Science Foundation of China （Grant No 10672147） and Natural Science Foundation of Zhejiang Forestry University, China （Grant No 2006FR035）. Acknowledgments The authors are indebted to Professor Zhang J F for his helpful suggestions and fruitful discussions, and also express their sincere thanks to the editors and the anonymous referees for their constructive suggestions and kind help.
文摘Starting from the extended tanh-function method （ETM） based on the mapping method, the variable separation solutions of the （2＋1）-dimensional asymmetric Nizhnik Novikov Veselov （ANNV） system are derived. By further study, we find that these variable separation solutions are seemingly independent of but actually dependent on each other. Based on the variable separation solution and by choosing appropriate functions, some novel and interesting interactions between special solitons, such as bell-like compacton, peakon-like compacton and compacton-like semifoldon, are investigated.
文摘This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨ cklund transformation was first obtained, and then the richness of the localized coherent structures was found, which was caused by the entrance of two variable separated arbitrary functions, in the model. For some special choices of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, and ring solitons.
基金National Natural Science Foundation of China under Grant No.10675065the Science Research Foundation of the Education Department of Zhejiang Province under Grant No.20070979+1 种基金the Natural Science Foundation of Zhejiang Province under Grant No.Y604036the State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation\PLN0402
基金supported by the National Natural Science Foundation of China Nos.11775146 and 12105243the Natural Science Foundation of Zhejiang Province of China Grant No.LQ22A050002。
文摘A new(2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov(eANNV)equation is proposed by introducing the additional bilinear terms to the usual ANNV equation.Based on the independent transformation,the bilinear form of the eANNV equation is constructed.The lump wave is guaranteed by introducing a positive constant term in the quadratic function.Meanwhile,different class solutions of the eANNV equation are obtained by mixing the quadratic function with the exponential functions.For the interaction between the lump wave and one-soliton,the energy of the lump wave and one-soliton can transfer to each other at different times.The interaction between a lump and two-soliton can be obtained only by eliminating the sixth-order bilinear term.The dynamics of these solutions are illustrated by selecting the specific parameters in three-dimensional,contour and density plots.
