In this paper, a new alternating group explicit-implicit （nAGEI） scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation er...In this paper, a new alternating group explicit-implicit （nAGEI） scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation error in space and a convergence ratio faster than some known alternating methods such as ASEI and AGE. Comparison in accuracy with the AGEI and AGE methods is presented in the numerical experiment.展开更多
The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite ...The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete schemes.In this sequel,we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in[9].The key tool employed to effect our analysis is the dispersive reconstruction devel-oped by Karakashian and Makridakis[20]for related discontinuous Galerkin methods.We conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators.展开更多
The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the correspondi...The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.展开更多
This paper studies the H^(p)-H^(q)estimates of a class of oscillatory integrals related to dispersive equations{i■_(t)u_(t,x)=Q(D)(t,x),(t,x)■R×R^(n),u(0,x)=u_(0)(x),x■R,,under the assumption that the level hy...This paper studies the H^(p)-H^(q)estimates of a class of oscillatory integrals related to dispersive equations{i■_(t)u_(t,x)=Q(D)(t,x),(t,x)■R×R^(n),u(0,x)=u_(0)(x),x■R,,under the assumption that the level hypersurfaces are convex and of finite type.As applications,we obtain the decay estimates for the solutions of higher order homogeneous and inhomogeneous Schrodinger equations.展开更多
Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data ...Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data f in Sobolev space, we give the local and global Lq estimate for the maximal operator S; defined by Sφf（x） = sup0〈t〈1｜St,φf（x）｜, where St,φ f is the solution of equation （＊）. These estimates imply the a.e. convergence of the solution of equation （＊）.展开更多
For a function Ф satisfying some suitable growth conditions,consider the following general dispersive equation defined by{i■tu+Ф(√-△)u=0,u(x,0)=f(x),(x,t)∈R^(n)× R,f∈S(R^(n) where Ф(√-△)is a pseudo-diff...For a function Ф satisfying some suitable growth conditions,consider the following general dispersive equation defined by{i■tu+Ф(√-△)u=0,u(x,0)=f(x),(x,t)∈R^(n)× R,f∈S(R^(n) where Ф(√-△)is a pseudo-differential operator with symbol Ф(|ξ|).In the present paper,when the initial data f belongs to Sobolev space,we give the local and global weighted L^(q) estimate for the global maximal operator S^(**)Ф defined by S^(**)Фf(x)=sup_(t∈R)|S_(t,Ф)f(x)|,where S_(t,Ф)f(x)=(2π)^(-n)∫_(R^(n)e^(ix·ζ+itФ(|ζ+|)f(ζ)dζ is a formal solution of the equation(*).展开更多
Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming t...Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming thatФsatisfies suitable growth conditions and the initial data in H^s(R^n),we bound the Hausdorff dimension of the sets on which the pointwise convergence of solutions to the dispersive equations(*)fails.These upper bounds of Hausdorff dimension shall be obtained via the Kolmogorov-Seliverstov-Plessner method.展开更多
This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous ba...This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.展开更多
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral fo...A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.展开更多
New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave sol...New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.展开更多
We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane ...We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane system corresponding to the GMDWW equation. By using the special orbits in the phase portraits, we analyze the existence of the traveling wave solutions. When some parameter takes special values, we obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation.展开更多
By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave e...By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.展开更多
A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued...A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.展开更多
For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exa...For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.展开更多
In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions...In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions of HDNLS equation are constructed by using the modified Darboux transformation method.The explicit first and secondorder rogue wave solutions are presented under the plane wave seeding solution background.The nonlinear dynamics and properties of rogue waves are discussed by analyzing the obtained rational solutions.The influence of little perturbation on the rogue waves is discussed with the help of graphical simulation.展开更多
By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact...By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.展开更多
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations....In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.展开更多
A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics.As an application of this method,we study the(2+1)-dimensional di...A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics.As an application of this method,we study the(2+1)-dimensional dispersive long wave equation.With the aid of computerized symbolic computation,a number of doubly periodic wave solutions expressed by various Jacobi elliptic functions are obtained.In the limit cases,the solitary wave solutions are derived as well.展开更多
By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given...By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.展开更多
In this paper, the separation transformation approach is extended to the （N ＋ 1）-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of SHe s...In this paper, the separation transformation approach is extended to the （N ＋ 1）-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of SHe superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obta/ned and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the （N ＋ 1）-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N 〉 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.展开更多
基金National Natural Science Foundation of China (No.10671113)
文摘In this paper, a new alternating group explicit-implicit （nAGEI） scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation error in space and a convergence ratio faster than some known alternating methods such as ASEI and AGE. Comparison in accuracy with the AGEI and AGE methods is presented in the numerical experiment.
基金This work was supported in part by the National Science Foundation under grant DMS-1620288。
文摘The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete schemes.In this sequel,we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in[9].The key tool employed to effect our analysis is the dispersive reconstruction devel-oped by Karakashian and Makridakis[20]for related discontinuous Galerkin methods.We conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators.
文摘The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.
基金supported by NSFC(No.12471092)the Natural Science Foundation of Hubei Province(No.2023AFB1056)。
文摘This paper studies the H^(p)-H^(q)estimates of a class of oscillatory integrals related to dispersive equations{i■_(t)u_(t,x)=Q(D)(t,x),(t,x)■R×R^(n),u(0,x)=u_(0)(x),x■R,,under the assumption that the level hypersurfaces are convex and of finite type.As applications,we obtain the decay estimates for the solutions of higher order homogeneous and inhomogeneous Schrodinger equations.
基金The authors would like to express their deep gratitude to the referees for their very careful reading. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371057, 11471033, 11571160, 11661061）, the Inner Mongolia University Scientific Research Projects （No. NJZZ16234）, and the Natural Science Foundation of Inner Mongolia （No. 2015MS0108）.
文摘Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data f in Sobolev space, we give the local and global Lq estimate for the maximal operator S; defined by Sφf（x） = sup0〈t〈1｜St,φf（x）｜, where St,φ f is the solution of equation （＊）. These estimates imply the a.e. convergence of the solution of equation （＊）.
基金supported by the National Natural Science Foundation of China(Nos.11871096,12071473,11661061,11761054)by the Natural Science Foundation of Inner Mongolia(Nos.2019MS01003,2021MS01001)Inner Mongolia University scientific research projects(Nos.NJZY19186,NJZZ21050)。
文摘For a function Ф satisfying some suitable growth conditions,consider the following general dispersive equation defined by{i■tu+Ф(√-△)u=0,u(x,0)=f(x),(x,t)∈R^(n)× R,f∈S(R^(n) where Ф(√-△)is a pseudo-differential operator with symbol Ф(|ξ|).In the present paper,when the initial data f belongs to Sobolev space,we give the local and global weighted L^(q) estimate for the global maximal operator S^(**)Ф defined by S^(**)Фf(x)=sup_(t∈R)|S_(t,Ф)f(x)|,where S_(t,Ф)f(x)=(2π)^(-n)∫_(R^(n)e^(ix·ζ+itФ(|ζ+|)f(ζ)dζ is a formal solution of the equation(*).
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11661061,11761054)the Inner Mongolia University Scientific Research Projects(No.NJZY19186)the Natural Science Foundation of Inner Mongolia(No.2019MS01003).
文摘Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming thatФsatisfies suitable growth conditions and the initial data in H^s(R^n),we bound the Hausdorff dimension of the sets on which the pointwise convergence of solutions to the dispersive equations(*)fails.These upper bounds of Hausdorff dimension shall be obtained via the Kolmogorov-Seliverstov-Plessner method.
文摘This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.
文摘A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx16
文摘New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11361069 and 11775146).
文摘We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane system corresponding to the GMDWW equation. By using the special orbits in the phase portraits, we analyze the existence of the traveling wave solutions. When some parameter takes special values, we obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation.
基金The project supported by China Postdoctoral Science Foundation, Natural Science Foundation of Zhejiang Province of China under Grant No. Y604056, and Doctor Foundation of Ningbo City under Grant No. 2005A610030
文摘By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.
基金supported in part by National Natural Science Foundation of China (Grant No 10772110)
文摘A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272071, the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, and the Key Academic Discipline of Zhejiang Province under Grant No. 200412.The authors are in debt to Prof. J.F. Zhang and Dr. W.H. Huang for their helpful suggestions and fruitful discussions.
文摘For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.
基金Supported by the National Natural Science Foundation of China under Grant No.11071164Innovation Program of Shanghai Municipal Education Commission under Grant Nos.12YZ105 and 13ZZ118+1 种基金the Foundation of University Young Teachers Training Program of Shanghai Municipal Education Commission under Grant No.slg11029the National Natural Science Foundation of China under Grant No.11171220
文摘In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions of HDNLS equation are constructed by using the modified Darboux transformation method.The explicit first and secondorder rogue wave solutions are presented under the plane wave seeding solution background.The nonlinear dynamics and properties of rogue waves are discussed by analyzing the obtained rational solutions.The influence of little perturbation on the rogue waves is discussed with the help of graphical simulation.
基金Supported by the Natural Science Foundation of Education Committee of Henan Province（2003110003）
文摘By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.
文摘In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
基金The project supported in part by National Natural Science Foundation of China under Grant No.10272071the Science Research Foundation of Huzhou University under Grant No.KX21025
文摘A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics.As an application of this method,we study the(2+1)-dimensional dispersive long wave equation.With the aid of computerized symbolic computation,a number of doubly periodic wave solutions expressed by various Jacobi elliptic functions are obtained.In the limit cases,the solitary wave solutions are derived as well.
基金Supported by the Natural Science Foundation of China under Grant No. 10735030Ningbo Natural Science Foundation under Grant No. 2008A610017+3 种基金National Basic Research Program of China (973 Program 2007CB814800)Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)K.C. Wong Magna Fund in Ningbo University
文摘By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.
基金Supported by NSFC for Young Scholars under Grant No.11101166Tianyuan Youth Foundation of Mathematics under Grant No.11126244+1 种基金Youth PhD Development Fund of CUFE 121 Talent Cultivation Project under Grant No.QBJZH201002Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No.KM201110772017
文摘In this paper, the separation transformation approach is extended to the （N ＋ 1）-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of SHe superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obta/ned and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the （N ＋ 1）-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N 〉 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.
