The dressing method based on the 2×2 matrix■-problem is generalized to study the complex modified KdV equation(cmKdV).Through two linear constraint equations,the spatial and time spectral problems related to the...The dressing method based on the 2×2 matrix■-problem is generalized to study the complex modified KdV equation(cmKdV).Through two linear constraint equations,the spatial and time spectral problems related to the cmKdV equation are derived.The gauge equivalence between the cmKdV equation and the Heisenberg chain equation is obtained.Using a recursive operator,a hierarchy of cmKdV with source is proposed.On the basis of the■-equation,the N-solition solutions of the cmKdV equation are obtained by selecting the appropriate spectral transformation matrix.Furthermore,we get explicit one-soliton and two-soliton solutions.展开更多
In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’...In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’s function of its Lax representation.Based on solving the ■ equation and choosing the proper spectral transformation,the solution of the DJKM equation is constructed.Furthermore,the more general solution of the DJKM equation can be also obtained by ensuring the evolution of the time spectral data.展开更多
We generalize the■-dressing method to investigate a(2+1)-dimensional lattice,which can be regarded as a forced(2+1)-dimensional discrete three-wave equation.The soliton solutions to the(2+1)-dimensional lattice are g...We generalize the■-dressing method to investigate a(2+1)-dimensional lattice,which can be regarded as a forced(2+1)-dimensional discrete three-wave equation.The soliton solutions to the(2+1)-dimensional lattice are given through constructing different symmetry conditions.The asymptotic analysis of one-soliton solution is discussed.For the soliton solution,the forces are zero.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12175111,11975131)the KC Wong Magna Fund in Ningbo University.
文摘The dressing method based on the 2×2 matrix■-problem is generalized to study the complex modified KdV equation(cmKdV).Through two linear constraint equations,the spatial and time spectral problems related to the cmKdV equation are derived.The gauge equivalence between the cmKdV equation and the Heisenberg chain equation is obtained.Using a recursive operator,a hierarchy of cmKdV with source is proposed.On the basis of the■-equation,the N-solition solutions of the cmKdV equation are obtained by selecting the appropriate spectral transformation matrix.Furthermore,we get explicit one-soliton and two-soliton solutions.
基金supported by National Natural Science Foundation of China under Grant Nos.12175111,11975131K C Wong Magna Fund in Ningbo University。
文摘In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’s function of its Lax representation.Based on solving the ■ equation and choosing the proper spectral transformation,the solution of the DJKM equation is constructed.Furthermore,the more general solution of the DJKM equation can be also obtained by ensuring the evolution of the time spectral data.
基金Project 11471295 was supported by the National Natural Science Foundation of Chinapartially supported by the President’s Endowed Professorship program of the University of Texas system.
文摘We generalize the■-dressing method to investigate a(2+1)-dimensional lattice,which can be regarded as a forced(2+1)-dimensional discrete three-wave equation.The soliton solutions to the(2+1)-dimensional lattice are given through constructing different symmetry conditions.The asymptotic analysis of one-soliton solution is discussed.For the soliton solution,the forces are zero.
