CAJ | 학술논문

从非局域非线性薛定谔方程出发，依据对数饱和型非线性介质中非线性折射率的变化规律，求出了1+1维双曲正割光束在强非局域对数饱和型非线性介质所对应的拉格朗日密度函数的近似表达式。在此基础上，利用变分法得到了光束各参量的演化方程。从光束各参量的演化方程出发，进一步得到了光束各参量的演化规律，并由此得到了一个临界束宽。当光束初始束宽等于临界束宽时，并且从束腰处入射时可以得到稳定的1+1维双曲正割型空间光孤子；在一般情形下，光束初始束宽不等于临界束宽时，得到了束宽振荡的1+1维双曲正割型空间呼吸子。
종비국역비선성설정악방정출발，의거대수포화형비선성개질중비선성절사솔적변화규률，구출료1+1유쌍곡정할광속재강비국역대수포화형비선성개질소대응적랍격랑일밀도함수적근사표체식。재차기출상，이용변분법득도료광속각삼량적연화방정。종광속각삼량적연화방정출발，진일보득도료광속각삼량적연화규률，병유차득도료일개림계속관。당광속초시속관등우림계속관시，병차종속요처입사시가이득도은정적1+1유쌍곡정할형공간광고자；재일반정형하，광속초시속관불등우림계속관시，득도료속관진탕적1+1유쌍곡정할형공간호흡자。
Based on non-local nonlinear Schr dinger equation, in light of the variation of nonlinear refractive index in loga-rithmic saturated nonlinear media, the approximate formula of Lagrangian density for 1+1D hyperbolic secant beams in strongly nonlocal logarithmic saturated nonlinear media is obtained. Based on this, evolution formula of light beam′s every variable are also derived using variational method. From these equations, the evolution laws of light beam′s every variable are derived futher and thus a critical beam width is gotten. When initial beam width is equal to the critical beam width and light beam is incident at the beam waist, we can get the stable 1+1D hyperbolic secant shaped spatial solitons. However, in the general cases, When initial beam width is not equal to the critical beam width , the 1+1D hyperbolic secant shaped spatial breathers with oscillating beam width can exist.