In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, ...In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.展开更多
Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meant...Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meantime it is shown that this leads to a direct reduction in the form of ordinary differential equation under some integrability conditions between the variable coefficients. Two different cases have been discussed, the search for solutions of those ordinary differential equations yielded many exact travelling and solitonic wave solutions in the form of hyperbolic and trigonometric functions under some constraints between the variable coefficients.展开更多
In this study,the generalized modified variable-coefficient KdV equation with external-force term(gvcmKdV)describing atmospheric blocking located in the mid-high latitudes over ocean is studied for integrability prope...In this study,the generalized modified variable-coefficient KdV equation with external-force term(gvcmKdV)describing atmospheric blocking located in the mid-high latitudes over ocean is studied for integrability property by using consistent Riccati expansion solvability and the necessary integrability conditions between the function coefficients are obtained.Moreover,several new solutions have been constructed for the gvcmKdV.Additionally,the classical direct similarity reduction method is used to re-duce the gvcmKdV to a nonlinear ordinary differential equation.Building on the solutions given in the previous literature for the reduced equation,many novel solitary and periodic wave solutions have been obtained for the gvcmKdV.展开更多
文摘In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.
文摘Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meantime it is shown that this leads to a direct reduction in the form of ordinary differential equation under some integrability conditions between the variable coefficients. Two different cases have been discussed, the search for solutions of those ordinary differential equations yielded many exact travelling and solitonic wave solutions in the form of hyperbolic and trigonometric functions under some constraints between the variable coefficients.
基金The author would like to thank the Deanship of Scientific Re-search,Majmaah University,Saudi Arabia,for funding this work under project No.R-2021-222.
文摘In this study,the generalized modified variable-coefficient KdV equation with external-force term(gvcmKdV)describing atmospheric blocking located in the mid-high latitudes over ocean is studied for integrability property by using consistent Riccati expansion solvability and the necessary integrability conditions between the function coefficients are obtained.Moreover,several new solutions have been constructed for the gvcmKdV.Additionally,the classical direct similarity reduction method is used to re-duce the gvcmKdV to a nonlinear ordinary differential equation.Building on the solutions given in the previous literature for the reduced equation,many novel solitary and periodic wave solutions have been obtained for the gvcmKdV.
