A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line...A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The interactions between a line soliton and a y-periodic soliton are classified into several types according to the phase shifts due to collision. There are two types of singular interactions. One is the resonant interaction that generates one line soliton while the other is the extremely repulsive or long-range interaction where two solitons interchange each other infinitely apart. Some new phenomena of interaction between two dromions are also reported in this paper, and detailed behaviors of interactions are illustrated both analytically and graphically.展开更多
Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study th...Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.展开更多
The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infinitec...The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infiniteconservation laws of the GNNV equation are obtained directly,without too much trick like Hirota’s bilinear method.展开更多
基金浙江省自然科学基金，浙江省宁波市博士基金，the State Kev Laboratory of Oil and Gas Reservoir Geology and Exploitation
文摘A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The interactions between a line soliton and a y-periodic soliton are classified into several types according to the phase shifts due to collision. There are two types of singular interactions. One is the resonant interaction that generates one line soliton while the other is the extremely repulsive or long-range interaction where two solitons interchange each other infinitely apart. Some new phenomena of interaction between two dromions are also reported in this paper, and detailed behaviors of interactions are illustrated both analytically and graphically.
文摘Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10735030,11075055,61021004,90718041,Shanghai Leading Academic Discipline Project (No. B412)Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)
文摘The elementary and systematic binary Bell polynomials method is applied to the generalized NizhnikNovikov-Veselov (GNNV) equation.The bilinear representation,bilinear B&cklund transformation,Lax pair and infiniteconservation laws of the GNNV equation are obtained directly,without too much trick like Hirota’s bilinear method.
