In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy.This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of so...We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy.This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of some earlier work.We also apply it to higher Weil-Petersson volumes and Witten’s r-spin intersection numbers.展开更多
In this paper, we define a new constrained multi-component KP （cMKP） hierarchy which contains the constrained KP （cKP） hierarchy as a special case. We derive the recursion operator of the constrained multi-compone...In this paper, we define a new constrained multi-component KP （cMKP） hierarchy which contains the constrained KP （cKP） hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.展开更多
The coupled Kadomtsev-Petviashvili equation is considered. It is shown that a Darboux transformation can be constructed by means of an elementary approach.
Infinitely many conservation laws for some （1＋1）-dimension soliton hierarchy with self-consistent sources are constructed from their corresponding Lax pairs directly. Three examples are given. Besides, infinitely m...Infinitely many conservation laws for some （1＋1）-dimension soliton hierarchy with self-consistent sources are constructed from their corresponding Lax pairs directly. Three examples are given. Besides, infinitely many conservation laws for Kadomtsev-Petviashvili （KP） hierarchy with self-consistent sources are obtained from the pseudo-differential operator and the Lax pair.展开更多
Most fundamental themes in mathematical physics and modern engineering are investigated by the closed form traveling wave solutions of nonlinear evolution equations.In our research,we ascertain abundant new closed for...Most fundamental themes in mathematical physics and modern engineering are investigated by the closed form traveling wave solutions of nonlinear evolution equations.In our research,we ascertain abundant new closed form traveling wave solution of the nonlinear integro-differential equations via Ito equation,integro-differential Sawada-Kotera equation,first integro-differential KP hierarchy equation and second integro-differential KP hierarchy equation by two variable(G/G,1/G)-expansion method with the help of computer package like Mathematica.Some shape of solutions like,bell profile solution,anti-king profile solution,soliton profile solution,periodic profile solution etc.are obtain in this investigation.Trigonometric function solution,hyperbolic function solution and rational function solution are established by using our eminent method and comparing with our results to all of the well-known results which are given in the literature.By means of free parameters,plentiful solitary solutions are derived from the exact traveling wave solutions.The method can be easier and more applicable to investigate such type of nonlinear evolution models.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(2015QNA43)
文摘In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
基金Supported by NSFC grants(Grant Nos.11171174,11661131005 and 11890662)。
文摘We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy.This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of some earlier work.We also apply it to higher Weil-Petersson volumes and Witten’s r-spin intersection numbers.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11571192,11671219)K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we define a new constrained multi-component KP （cMKP） hierarchy which contains the constrained KP （cKP） hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.
基金Supported by the National Natural Science Foundation of China under Grant No 10671206.
文摘The coupled Kadomtsev-Petviashvili equation is considered. It is shown that a Darboux transformation can be constructed by means of an elementary approach.
基金supported by the National Natural Science Foundation of China (Grant Nos.10371070, 10671121)the Shanghai Leading Academic Discipline Project (Grant No.J50101)the President Foundation of East China Institute of Technology (Grant No.DHXK0810)
文摘Infinitely many conservation laws for some （1＋1）-dimension soliton hierarchy with self-consistent sources are constructed from their corresponding Lax pairs directly. Three examples are given. Besides, infinitely many conservation laws for Kadomtsev-Petviashvili （KP） hierarchy with self-consistent sources are obtained from the pseudo-differential operator and the Lax pair.
文摘Most fundamental themes in mathematical physics and modern engineering are investigated by the closed form traveling wave solutions of nonlinear evolution equations.In our research,we ascertain abundant new closed form traveling wave solution of the nonlinear integro-differential equations via Ito equation,integro-differential Sawada-Kotera equation,first integro-differential KP hierarchy equation and second integro-differential KP hierarchy equation by two variable(G/G,1/G)-expansion method with the help of computer package like Mathematica.Some shape of solutions like,bell profile solution,anti-king profile solution,soliton profile solution,periodic profile solution etc.are obtain in this investigation.Trigonometric function solution,hyperbolic function solution and rational function solution are established by using our eminent method and comparing with our results to all of the well-known results which are given in the literature.By means of free parameters,plentiful solitary solutions are derived from the exact traveling wave solutions.The method can be easier and more applicable to investigate such type of nonlinear evolution models.
