标题： 非线性薛定谔方程解的准经典近似典型的衰减渐进行为 显示英文标题

标题： Typical dropping asymptotics of quasiclassical approximations to solutions of the nonlinear Schrödinger equation

摘要： Formal asymptotics are substantiated that describe typical dropping cusp singularity of quasiclassical approximations to solutions of two cases of the integrable nonlinear Schrödinger equation $-i\varepsilon\Psi'_{t}=\varepsilon^2\Psi''_{xx}\pm2|\Psi| ^2\Psi$, where $\varepsilon$ is a small parameter. The substantiation uses the ideology and facts of the mathematical catastrophe theory and the part of the theorem of Yu. F. Korobeinik, concerning analytical as $h\to 0$ solutions $G(h,u)$ of the mixed type linear equation $hG''_{hh}=G''_{uu}$ to which the hodograph images of both cases of the systems of equations of these quasiclassical approximations are equivalent. 显示英文摘要

摘要： Formal asymptotics are substantiated that describe typical dropping cusp singularity of quasiclassical approximations to solutions of two cases of the integrable nonlinear Schr\"odinger equation $-i\varepsilon\Psi'_{t}=\varepsilon^2\Psi''_{xx}\pm2|\Psi| ^2\Psi$, where $\varepsilon$ is a small parameter. The substantiation uses the ideology and facts of the mathematical catastrophe theory and the part of the theorem of Yu. F. Korobeinik, concerning analytical as $h\to 0$ solutions $G(h,u)$ of the mixed type linear equation $hG''_{hh}=G''_{uu}$ to which the hodograph images of both cases of the systems of equations of these quasiclassical approximations are equivalent.