局部齐次非线性Schroedinger方程的长孤子解
Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schroedinger Equation
摘要：
我们发现了薛定谔方程的无势Stenflo-Sabatier-Doebner-Goldin非线性修正的5参数族的一类新的孤子解.与{ \cosh [b（x-kt）]}^{-a} \exp [i（kx-ft）]等“通常的”孤子不同，新的{ \em长孤子}（FLS）是具有连续一阶导数的非解析函数，其导数仅在有限空间区域内不为零。最简单的一维示例是等于{ \cos [g（x-kt）]}^{1+d} \exp [i（kx-ft）]（其中d>0）的函数，|x-kt| <π/（2g），对于|x-kt|>π/（2g）。当非线性参数超过某一临界值时，FLS存在，而“通常”孤子存在。
英文摘要：
We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schrödinger equation. In contradistinction to the "usual'' solitons like {\cosh[b(x-kt)]}^{-a}\exp[i(kx-ft)], the new {\em Finite-Length Solitons} (FLS) are nonanalytical functions with continuous first derivatives, which are different from zero only inside some finite regions of space. The simplest one-dimensional example is the function which is equal to {\cos[g(x-kt)]}^{1+d}\exp[i(kx-ft)] (with d>0) for |x-kt|<π/(2g), being identically equal to zero for |x-kt|>π/(2g). The FLS exist even in the case of a weak nonlinearity, whereas the ``usual'' solitons exist provided the nonlinearity parameters surpass some critical values.
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