In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the B...In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.展开更多
This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the （w/g）-expansion method, which can be thought of as the generalization of ...This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the （w/g）-expansion method, which can be thought of as the generalization of （G＇/G）-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.展开更多
In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is prop...In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.展开更多
Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Pain...Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.展开更多
The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. ...The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.展开更多
We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete（G /G）-expansion method, we solve ...We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete（G /G）-expansion method, we solve the nonlinear differential–difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.展开更多
In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental preci...In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earth's rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.展开更多
Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main aim is to use a new method known as the(G′/G)method to exhibit the effects of dust cha...Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main aim is to use a new method known as the(G′/G)method to exhibit the effects of dust charge fluctuations on the evolution of nonlinear waves. The coherent features of the shock and solitary waves along with the generation of high-energy waves have been amplified through the solution of the Korteweg–de Vries–Burgers equation,and the different natures of the waves were found successfully. Results are discussed graphically with the thoughtful choice of typical plasma parameters from different space plasma environments, exactly those found in cosmic dusty plasmas laden in ionospheric auroral region,radial spokes of Saturn's rings, planetary nebulae and solar F-corona region. All conclusions are in good accordance with the actual occurrences and could be of interest to further investigations of space. Moreover, the applicability of the present method is hoped to be a great enhancement by its use as ingenious mechanism used to evaluate the soliton dynamics and Burgers shock waves.展开更多
文摘In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.
文摘This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the （w/g）-expansion method, which can be thought of as the generalization of （G＇/G）-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.
文摘In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.
基金Project supported by the National Key Basic Research Project of China (Grant No. 2004CB318000)the National Natural Science Foundation of China (Grant No. 10771072)
文摘Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.
基金Project supported by the National Nature Science Foundation of China （Grant No 49894190） of the Chinese Academy of Science （Grant No KZCXI-sw-18）, and Knowledge Innovation Program.
文摘The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.
基金supported by the Scientific Commission/ENS/University of Maroua 2013AM is grateful to the Abdus Salam International Center for Theoretical Physics(ICTP),Trieste,Italy through the Associate Program for financial support
文摘We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete（G /G）-expansion method, we solve the nonlinear differential–difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575160 and 11805074)the Postdoctoral Science Foundation of China(Grant Nos.2017M620308 and 2018T110750).
文摘In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earth's rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.
文摘Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main aim is to use a new method known as the(G′/G)method to exhibit the effects of dust charge fluctuations on the evolution of nonlinear waves. The coherent features of the shock and solitary waves along with the generation of high-energy waves have been amplified through the solution of the Korteweg–de Vries–Burgers equation,and the different natures of the waves were found successfully. Results are discussed graphically with the thoughtful choice of typical plasma parameters from different space plasma environments, exactly those found in cosmic dusty plasmas laden in ionospheric auroral region,radial spokes of Saturn's rings, planetary nebulae and solar F-corona region. All conclusions are in good accordance with the actual occurrences and could be of interest to further investigations of space. Moreover, the applicability of the present method is hoped to be a great enhancement by its use as ingenious mechanism used to evaluate the soliton dynamics and Burgers shock waves.
