The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific...The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations(ODEs)such that the resulting systems can be efficiently handled by computer algebra systems.As an accomplishment,the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed.In the end,the stability analysis for the NLWWE is investigated through the linear stability scheme.展开更多
The present paper studies the unstable nonlinear Schr¨odinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schr¨odin...The present paper studies the unstable nonlinear Schr¨odinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schr¨odinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schr¨odinger equation and its modified form are formally obtained.展开更多
Investigated in the present paper is a fifth-order nonlinear evolution(FONLE)equation,known as a nonlinear water wave(NLWW)equation,with applications in the applied sciences.More precisely,a traveling wave hypothesis ...Investigated in the present paper is a fifth-order nonlinear evolution(FONLE)equation,known as a nonlinear water wave(NLWW)equation,with applications in the applied sciences.More precisely,a traveling wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain.The Kudryashov methods(KMs)are then adopted as leading techniques to construct specific wave structures of the governing model which are classified as W-shaped and other solitons.In the end,the effect of changing the coefficients of nonlinear terms on the dynamical features of W-shaped and other solitons is investigated in detail for diverse groups of the involved parameters.展开更多
The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Er...The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Eringen's nonlocal elasticity theory, a nonclassical model is developed. Using the Galerkin method(GM), the governing equation which is a nonlinear partial differential equation(NLPDE) of the fourth order is converted to a nonlinear ordinary differential equation(NLODE) in the time domain. Then, the reduced NLODE is solved analytically by means of the homotopy analysis method. At the end, the effects of model parameters as well as the nonlocal parameter on the deflection, nonlinear frequency, and dynamic pull-in voltage are explored.展开更多
文摘The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations(ODEs)such that the resulting systems can be efficiently handled by computer algebra systems.As an accomplishment,the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed.In the end,the stability analysis for the NLWWE is investigated through the linear stability scheme.
文摘The present paper studies the unstable nonlinear Schr¨odinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schr¨odinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schr¨odinger equation and its modified form are formally obtained.
文摘Investigated in the present paper is a fifth-order nonlinear evolution(FONLE)equation,known as a nonlinear water wave(NLWW)equation,with applications in the applied sciences.More precisely,a traveling wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain.The Kudryashov methods(KMs)are then adopted as leading techniques to construct specific wave structures of the governing model which are classified as W-shaped and other solitons.In the end,the effect of changing the coefficients of nonlinear terms on the dynamical features of W-shaped and other solitons is investigated in detail for diverse groups of the involved parameters.
文摘The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Eringen's nonlocal elasticity theory, a nonclassical model is developed. Using the Galerkin method(GM), the governing equation which is a nonlinear partial differential equation(NLPDE) of the fourth order is converted to a nonlinear ordinary differential equation(NLODE) in the time domain. Then, the reduced NLODE is solved analytically by means of the homotopy analysis method. At the end, the effects of model parameters as well as the nonlocal parameter on the deflection, nonlinear frequency, and dynamic pull-in voltage are explored.
