Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. ...Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, Δn2 （I）≈ρ（b0＋ b1f - b2 f^2 with b2/b1 〉 0 is assumed. Furthermore, instead of the wave function Ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If the frequency shift of wave number β satisfies 0 〈 4（β - ρbo/μ） 〈 3η0/8α, the bistable state soliton solution is stable against perturbation. It should be emphasized that the soliton solution arising from a parabolic-symmetry response kernel is trivial. The sufficient condition for the existence of bistable state soliton solution b2/b1〉 0 has been demonstrated.展开更多
Assume that an oasis and its surrounding desert consist of an isolated system without mass and energy exchange with the outer environment.The characteristics of oasis evolution have been explored under the condition o...Assume that an oasis and its surrounding desert consist of an isolated system without mass and energy exchange with the outer environment.The characteristics of oasis evolution have been explored under the condition of system energy conservation.The results show that oasis evolves with two equilibrium states.The first equilibrium suggests a stable expansive and an unstable degraded oasis whereas the second equilibrium indicates a stable shrink and an unstable increase of the oasis area.If one equilibrium state is unstable,the components of the isolated system(oasis and desert) would tend to be no energy exchange and they each reach to energy balance respectively.Oasis would maintain its initial area in this case.Further analyses point out that the two equilibrium states have completely different characteristics.In the first equilibrium state,a higher vegetation albedo,lower soil albedo and larger canopy resistance,and direr soil both contribute to the oasis area expansion,accompanying an excessive large desert soil and vegetation canopy temperature difference(SCTD).In the second equilibrium state,however,a lower vegetation albedo,higher soil albedo and small canopy resistance,and wetter soil benefit the oasis area to stay near its initial value,following a moderate SCTD.The convergent trajectories of the initial values in phase space are influenced by the separatrices of the equilibrium points.Higher temperature is an advantage factor for initial values convergent to the oasis expansion solution.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10574163
文摘Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, Δn2 （I）≈ρ（b0＋ b1f - b2 f^2 with b2/b1 〉 0 is assumed. Furthermore, instead of the wave function Ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If the frequency shift of wave number β satisfies 0 〈 4（β - ρbo/μ） 〈 3η0/8α, the bistable state soliton solution is stable against perturbation. It should be emphasized that the soliton solution arising from a parabolic-symmetry response kernel is trivial. The sufficient condition for the existence of bistable state soliton solution b2/b1〉 0 has been demonstrated.
基金supported by the National Basic Research Program of China(Grant No.2014CB953903)the Fundamental Research Funds for the Central Universities(Grant No.2013YB45)
文摘Assume that an oasis and its surrounding desert consist of an isolated system without mass and energy exchange with the outer environment.The characteristics of oasis evolution have been explored under the condition of system energy conservation.The results show that oasis evolves with two equilibrium states.The first equilibrium suggests a stable expansive and an unstable degraded oasis whereas the second equilibrium indicates a stable shrink and an unstable increase of the oasis area.If one equilibrium state is unstable,the components of the isolated system(oasis and desert) would tend to be no energy exchange and they each reach to energy balance respectively.Oasis would maintain its initial area in this case.Further analyses point out that the two equilibrium states have completely different characteristics.In the first equilibrium state,a higher vegetation albedo,lower soil albedo and larger canopy resistance,and direr soil both contribute to the oasis area expansion,accompanying an excessive large desert soil and vegetation canopy temperature difference(SCTD).In the second equilibrium state,however,a lower vegetation albedo,higher soil albedo and small canopy resistance,and wetter soil benefit the oasis area to stay near its initial value,following a moderate SCTD.The convergent trajectories of the initial values in phase space are influenced by the separatrices of the equilibrium points.Higher temperature is an advantage factor for initial values convergent to the oasis expansion solution.
