This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case ...This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).展开更多
In this paper,using the reductive perturbation method combined with the PLK method and two-parameter expansions,we treat the problem of head-on collision between two solitary waves described by the generalized Kortewe...In this paper,using the reductive perturbation method combined with the PLK method and two-parameter expansions,we treat the problem of head-on collision between two solitary waves described by the generalized Korteweg-de Vries equation (the gKdV equation) and obtain its second-order approximate solution.The results show that after the collision,the gKdV solitary waves preserve their profiles and during the collision,the maximum amplitute is the linear superposition of two maximum amplitudes of the impinging solitary waves.展开更多
Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with...Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV展开更多
By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general (2+1)-dimensional Korteweg de Vries system (GKdV) are derived.Based on the derivedsolita...By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general (2+1)-dimensional Korteweg de Vries system (GKdV) are derived.Based on the derivedsolitary wave excitation,we obtain some special peakon excitations and fractal dromions in this short note.展开更多
In waves dynamics, Generalized Kortewegde Vries (gKdV) equation and Sawada-Kotera equation (Ske) have been used to study nonlinear acoustic waves, an inharmonic lattice and Alfven waves in a collisionless plasma, and ...In waves dynamics, Generalized Kortewegde Vries (gKdV) equation and Sawada-Kotera equation (Ske) have been used to study nonlinear acoustic waves, an inharmonic lattice and Alfven waves in a collisionless plasma, and a lot of more important physical phenomena. In this paper, the simple equation method (SEM) is used to obtain new traveling wave solutions of gKdv and Ske. The physical properties of the obtained solutions are graphically illustrated using suitable parameters. The computational simplicity of the proposed method shows the robustness and efficiency of SEM.展开更多
In this paper, based on Lax pair of Riccati form of the generalized KdV(GKdV) equation with external force term, a new auto-Darboux transformation (ADT) is derived. As the application of the ADT, only if integration i...In this paper, based on Lax pair of Riccati form of the generalized KdV(GKdV) equation with external force term, a new auto-Darboux transformation (ADT) is derived. As the application of the ADT, only if integration is needed, a series of explicit analytic solutions can be obtained, which contain solitary-like wave solutions. This method may be important for seeking more new and physical signficant analytic solutions of nonlinear evolution equations.展开更多
The present article investigates the effect of Coriolis constant on the solution of the Geophysical Korteweg-de Vries(gKdV)equation.As such,the Homotopy Perturbation Method(HPM)has been applied here for solving the no...The present article investigates the effect of Coriolis constant on the solution of the Geophysical Korteweg-de Vries(gKdV)equation.As such,the Homotopy Perturbation Method(HPM)has been applied here for solving the nonlinear gKdV equation.Present results are compared with existing results that are available in the literature and they are found to be in good agreement.Then the Coriolis term has been considered in terms of the interval to form interval Geophysical Korteweg-de Vries(IgKdV)equation.IgKdV equation has been solved by HPM to analyse the effect of Coriolis.From this analysis,it has been concluded that the constant of Coriolis is directly proportional to wave height and inversely proportional to wavelength.The presence of the Coriolis term in gKdV equation has a remarkable change in the shape of the solution.展开更多
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802)。
文摘This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).
文摘In this paper,using the reductive perturbation method combined with the PLK method and two-parameter expansions,we treat the problem of head-on collision between two solitary waves described by the generalized Korteweg-de Vries equation (the gKdV equation) and obtain its second-order approximate solution.The results show that after the collision,the gKdV solitary waves preserve their profiles and during the collision,the maximum amplitute is the linear superposition of two maximum amplitudes of the impinging solitary waves.
基金Project supported by the National Natural Science Foundation of China （Grant No 10172056）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y604106）, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, the Scientific Research Foundation of Zhejiang Provincial Education Department of China （Grant No 20070568） and the Natural Science Foundation of Zhejiang Lishui University （Grant No KZ04008）.
文摘Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y604106the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ05010
文摘By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general (2+1)-dimensional Korteweg de Vries system (GKdV) are derived.Based on the derivedsolitary wave excitation,we obtain some special peakon excitations and fractal dromions in this short note.
文摘In waves dynamics, Generalized Kortewegde Vries (gKdV) equation and Sawada-Kotera equation (Ske) have been used to study nonlinear acoustic waves, an inharmonic lattice and Alfven waves in a collisionless plasma, and a lot of more important physical phenomena. In this paper, the simple equation method (SEM) is used to obtain new traveling wave solutions of gKdv and Ske. The physical properties of the obtained solutions are graphically illustrated using suitable parameters. The computational simplicity of the proposed method shows the robustness and efficiency of SEM.
基金Supported by the National Natural Science Foundation of China under the Grant(19572022)Doctoral Foundation of Education Mini
文摘In this paper, based on Lax pair of Riccati form of the generalized KdV(GKdV) equation with external force term, a new auto-Darboux transformation (ADT) is derived. As the application of the ADT, only if integration is needed, a series of explicit analytic solutions can be obtained, which contain solitary-like wave solutions. This method may be important for seeking more new and physical signficant analytic solutions of nonlinear evolution equations.
基金The authors are thankful to Board of Research in Nu-clear Sciences(BRNS),Mumbai,India(Grant Number:36(4)/40/46/2014-BRNS)for the support and funding to carry out the present research work.
文摘The present article investigates the effect of Coriolis constant on the solution of the Geophysical Korteweg-de Vries(gKdV)equation.As such,the Homotopy Perturbation Method(HPM)has been applied here for solving the nonlinear gKdV equation.Present results are compared with existing results that are available in the literature and they are found to be in good agreement.Then the Coriolis term has been considered in terms of the interval to form interval Geophysical Korteweg-de Vries(IgKdV)equation.IgKdV equation has been solved by HPM to analyse the effect of Coriolis.From this analysis,it has been concluded that the constant of Coriolis is directly proportional to wave height and inversely proportional to wavelength.The presence of the Coriolis term in gKdV equation has a remarkable change in the shape of the solution.
