For waves in inhomogeneous media,variable-coefficient evolution equations can arise.It is known that the Manakov model can derive two models for propagation in uniform optical fibers.If the fiber is nonuniform,one wou...For waves in inhomogeneous media,variable-coefficient evolution equations can arise.It is known that the Manakov model can derive two models for propagation in uniform optical fibers.If the fiber is nonuniform,one would expect that the coefficients in the model are not constants.We present a variable-coefficient Manakov model and derive its Lax pair using the generalized dressing method.As an application of the generalized dressing method,soliton solutions of the variable-coefficient Manakov model are obtained.展开更多
Based on the nonlinearization of Lax pairs, the Korteweg-de Vries （KdV） soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of th...Based on the nonlinearization of Lax pairs, the Korteweg-de Vries （KdV） soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of the elliptic coordinates. By applying the Abel-Jacobi coordinates on a Riemann surface of hyperelliptic curve, the resulting Hamiltonian flows as well as the KdV soliton hierarchy are ultimately reduced into linear superpositions, expressed by the Abel-Jacobi variables.展开更多
By introducing a SchrSdinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Ha...By introducing a SchrSdinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Hamiltonian system, which is completely integrable in the Liouville sense.展开更多
Utilizing the Wronskian technique,a new Wronskian representation is proposed for a variable-coefficient Kadomtsev–Petviashvili(vcKP)equation.Furthermore,some particular forms of Wronskian determinant solutions,includ...Utilizing the Wronskian technique,a new Wronskian representation is proposed for a variable-coefficient Kadomtsev–Petviashvili(vcKP)equation.Furthermore,some particular forms of Wronskian determinant solutions,includingN-soliton solutions,trigonometric function solutions and rational solutions,are obtained for the equation.展开更多
The dressing method,based on the local 3×3 matrix ∂-problem,is extended to study the Sasa–Satsuma equation with self-consistent sources.The explicit solutions,including one-soliton and two-soliton solutions,are ...The dressing method,based on the local 3×3 matrix ∂-problem,is extended to study the Sasa–Satsuma equation with self-consistent sources.The explicit solutions,including one-soliton and two-soliton solutions,are given by virtue of the properties of the Cauchy matrix.展开更多
The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth ...The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.展开更多
基金Supported by City University of Hong Kong under Grant No 7002366the National Natural Science Foundation of China under Grant No 10871182.
文摘For waves in inhomogeneous media,variable-coefficient evolution equations can arise.It is known that the Manakov model can derive two models for propagation in uniform optical fibers.If the fiber is nonuniform,one would expect that the coefficients in the model are not constants.We present a variable-coefficient Manakov model and derive its Lax pair using the generalized dressing method.As an application of the generalized dressing method,soliton solutions of the variable-coefficient Manakov model are obtained.
基金The project supported by National Natural Science Foundation of China under Grant No. 10471132 and the Special Foundation for.the State Key Basic Research Project ＂Nonlinear Science＂
文摘Based on the nonlinearization of Lax pairs, the Korteweg-de Vries （KdV） soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of the elliptic coordinates. By applying the Abel-Jacobi coordinates on a Riemann surface of hyperelliptic curve, the resulting Hamiltonian flows as well as the KdV soliton hierarchy are ultimately reduced into linear superpositions, expressed by the Abel-Jacobi variables.
文摘By introducing a SchrSdinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Hamiltonian system, which is completely integrable in the Liouville sense.
基金Supported by the National Natural Science Foundation of China under Grant No 11171312.
文摘Utilizing the Wronskian technique,a new Wronskian representation is proposed for a variable-coefficient Kadomtsev–Petviashvili(vcKP)equation.Furthermore,some particular forms of Wronskian determinant solutions,includingN-soliton solutions,trigonometric function solutions and rational solutions,are obtained for the equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11001250 and 11171312.
文摘The dressing method,based on the local 3×3 matrix ∂-problem,is extended to study the Sasa–Satsuma equation with self-consistent sources.The explicit solutions,including one-soliton and two-soliton solutions,are given by virtue of the properties of the Cauchy matrix.
基金the Youth Fund of Zhoukou Normal University(ZKnuqn200606)
文摘The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.
