Soliton solutions, rational solutions, Matveev solutions, complexitons and interaction solutions of the AKNS equation are derived through a matrix method for constructing double Wronskian entries. The latter three sol...Soliton solutions, rational solutions, Matveev solutions, complexitons and interaction solutions of the AKNS equation are derived through a matrix method for constructing double Wronskian entries. The latter three solutions are novel. Moreover, rational solutions of the nonlinear Schrodinger equation are obtained by reduction.展开更多
Using the methods of dynamical systems for the (n+ 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions axe obtained. Fo...Using the methods of dynamical systems for the (n+ 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions axe obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.展开更多
This paper solves the integrable CH-γequation for analytical multiple soliton solutions with the Darboux transformation method.Some properties of the soliton solutions are different from the CH equation.
An algebraic structure of discrete zero curvature equations is established for integrable coupling systems associated with semi-direct sums of Lie algebras. As an application example of this algebraic structure, a τ-...An algebraic structure of discrete zero curvature equations is established for integrable coupling systems associated with semi-direct sums of Lie algebras. As an application example of this algebraic structure, a τ-symmetry algebra for the Volterra lattice integrable couplings is engendered from this theory.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10371070, 10671121)
文摘Soliton solutions, rational solutions, Matveev solutions, complexitons and interaction solutions of the AKNS equation are derived through a matrix method for constructing double Wronskian entries. The latter three solutions are novel. Moreover, rational solutions of the nonlinear Schrodinger equation are obtained by reduction.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 11671179)the Natural Science Foundation of Yunnan Province (Grant No. 2005A0092M).
文摘Using the methods of dynamical systems for the (n+ 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions axe obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.
基金the National Natural Science Foundation of China (Grant No.10401022)the Research Grants Council of Hong Kong
文摘This paper solves the integrable CH-γequation for analytical multiple soliton solutions with the Darboux transformation method.Some properties of the soliton solutions are different from the CH equation.
基金supported by the National Key Basic Research Project of China (Grant No. 2004CB318000)the Research Foundation of Hubei Provincial Department of Education (Grant No. D20082602)
文摘An algebraic structure of discrete zero curvature equations is established for integrable coupling systems associated with semi-direct sums of Lie algebras. As an application example of this algebraic structure, a τ-symmetry algebra for the Volterra lattice integrable couplings is engendered from this theory.
