Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear....Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.展开更多
Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation is determined. It is proved that such kind of equation has no C-k( k greater than or equal to2) stab...Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation is determined. It is proved that such kind of equation has no C-k( k greater than or equal to2) stable solution by the fact that the strate transversale is a null set.展开更多
In this paper, by proving that the equations discussed here are l_simple (l≥1) by stratification theory, the unstability of the equations is proved. And the un_uniqueness of the solution of forced dissipative non_...In this paper, by proving that the equations discussed here are l_simple (l≥1) by stratification theory, the unstability of the equations is proved. And the un_uniqueness of the solution of forced dissipative non_linear system equations in atmospheric dynamics is used as an illustration for the result.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
文摘Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.
文摘Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation is determined. It is proved that such kind of equation has no C-k( k greater than or equal to2) stable solution by the fact that the strate transversale is a null set.
文摘In this paper, by proving that the equations discussed here are l_simple (l≥1) by stratification theory, the unstability of the equations is proved. And the un_uniqueness of the solution of forced dissipative non_linear system equations in atmospheric dynamics is used as an illustration for the result.
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.
