This paper gives the spectral representation of a class of （2＋1）-dimensional modified Kadomtsev-Petviashvili（m-KP） equation with a constant parameter. Its quasi-periodic solution is obtained in terms of Riemann t...This paper gives the spectral representation of a class of （2＋1）-dimensional modified Kadomtsev-Petviashvili（m-KP） equation with a constant parameter. Its quasi-periodic solution is obtained in terms of Riemann theta functions.展开更多
In this paper, a variable-coefficient modified Korteweg-de Vries （vc-mKdV） equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann the...In this paper, a variable-coefficient modified Korteweg-de Vries （vc-mKdV） equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented~ and it is also shown that the soliton solutions can be reduced from the periodic wave solutions.展开更多
In this paper,multi-periodic (quasi-periodic) wave solutions are constructed for the Boiti-Leon-Manna-Pempinelli(BLMP) equation by using Hirota bilinear method and Riemann theta function.At the same time,weanalyze in ...In this paper,multi-periodic (quasi-periodic) wave solutions are constructed for the Boiti-Leon-Manna-Pempinelli(BLMP) equation by using Hirota bilinear method and Riemann theta function.At the same time,weanalyze in details asymptotic properties of the multi-periodic wave solutions and give their asymptotic relations betweenthe periodic wave solutions and the soliton solutions.展开更多
In this paper,the bidirectional SK-Ramani equation is investigated by means of the extended homoclinic test approach and Riemann theta function method,respectively.Based on the Hirota bilinear method,exact solutions i...In this paper,the bidirectional SK-Ramani equation is investigated by means of the extended homoclinic test approach and Riemann theta function method,respectively.Based on the Hirota bilinear method,exact solutions including one-soliton wave solution are obtained by using the extended homoclinic approach and one-periodic wave solution is constructed by using the Riemann theta function method.A limiting procedure is presented to analyze in detail the relations between the one periodic wave solution and one-soliton solution.展开更多
Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-New...Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations.The Abel-Jacobi coordinates are introduced to straighten the flows,from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.展开更多
In this paper, we use the representation of the solutions of the focusing nonlinear Schrodinger equation we have constructed recently, in terms of wronskians;when we perform a special passage to the limit, we get quas...In this paper, we use the representation of the solutions of the focusing nonlinear Schrodinger equation we have constructed recently, in terms of wronskians;when we perform a special passage to the limit, we get quasi-rational solutions expressed as a ratio of two determinants. We have already construct breathers of orders N = 4, 5, 6 in preceding works;we give here the breather of order seven.展开更多
We construct the Hirota bilinear form of the nonlocal Boussinesq（nlBq） equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator togethe...We construct the Hirota bilinear form of the nonlocal Boussinesq（nlBq） equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.展开更多
Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann T...Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results and the consequences assuming RH are true.展开更多
基金Supported by the Special Funds for Major State Basic Research Projects(G2000077301)Supported by the doctoral foundation of Zhanjiang Normal University(ZL0601)
文摘This paper gives the spectral representation of a class of （2＋1）-dimensional modified Kadomtsev-Petviashvili（m-KP） equation with a constant parameter. Its quasi-periodic solution is obtained in terms of Riemann theta functions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10771196 and 10831003)the Innovation Project of Zhejiang Province of China(Grant No.T200905)
文摘In this paper, a variable-coefficient modified Korteweg-de Vries （vc-mKdV） equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented~ and it is also shown that the soliton solutions can be reduced from the periodic wave solutions.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1412800 the Innovation Program of Shanghai Municipal Education Commission under Grant No.10ZZ131
文摘In this paper,multi-periodic (quasi-periodic) wave solutions are constructed for the Boiti-Leon-Manna-Pempinelli(BLMP) equation by using Hirota bilinear method and Riemann theta function.At the same time,weanalyze in details asymptotic properties of the multi-periodic wave solutions and give their asymptotic relations betweenthe periodic wave solutions and the soliton solutions.
文摘In this paper,the bidirectional SK-Ramani equation is investigated by means of the extended homoclinic test approach and Riemann theta function method,respectively.Based on the Hirota bilinear method,exact solutions including one-soliton wave solution are obtained by using the extended homoclinic approach and one-periodic wave solution is constructed by using the Riemann theta function method.A limiting procedure is presented to analyze in detail the relations between the one periodic wave solution and one-soliton solution.
基金Supported by the Natural Science Foundation of China(Grant Nos.11547175,11271008)Supported by the Science and Technology Department of Henan Province(No.182102310978)Supported by the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China(Grant Nos.2017GGJS145,2014GGJS-195)
文摘Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations.The Abel-Jacobi coordinates are introduced to straighten the flows,from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.
文摘In this paper, we use the representation of the solutions of the focusing nonlinear Schrodinger equation we have constructed recently, in terms of wronskians;when we perform a special passage to the limit, we get quasi-rational solutions expressed as a ratio of two determinants. We have already construct breathers of orders N = 4, 5, 6 in preceding works;we give here the breather of order seven.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51579040,51379033,and 51522902)the National Basic Research Program of China(Grant No.2013CB036101)Liaoning Natural Science Foundation,China(Grant No.201602172)
文摘We construct the Hirota bilinear form of the nonlocal Boussinesq（nlBq） equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.
文摘Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results and the consequences assuming RH are true.
