标题： 新型孤子解 显示英文标题

标题： New types of soliton solutions

摘要： 我们宣布对Korteweg-deVries（KdV）方程的N-孤立子解在$N$趋于无穷时的极限进行详细研究。 我们的主要结果提供了新的KdV解类，特别是包括新型的类似孤立子（无反射）解。 作为副产品，我们解决了二维Schrödinger算子的逆谱问题，并显式构造了光滑且实值的势函数，这些势函数在非负实轴上产生纯绝对连续谱，并产生包含负实轴上任何预定可数且有界子集的特征值谱。 显示英文摘要

摘要： We announce a detailed investigation of limits of N-soliton solutions of the Korteweg-deVries (KdV) equation as $N$ tends to infinity. Our main results provide new classes of KdV-solutions including in particular new types of soliton-like (reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one-dimensional Schr\"odinger operators and explicitly construct smooth and real-valued potentials that yield a purely absolutely continuous spectrum on the nonnegative real axis and give rise to an eigenvalue spectrum that includes any prescribed countable and bounded subset of the negative real axis.