互反型高维可积Kaup-Newell系统  

Higher dimensional reciprocal integrable Kaup-Newell systems

作　　者：楼森岳[1] 郝夏芝 贾曼[1] Lou Sen-Yue;Hao Xia-Zhi;Jia Man(School of Physical Science and Technology,Ningbo University,Ningbo 315211,China;Faculty of Science,Zhejiang University of Technology,Hangzhou 310014,China)

机构地区：[1]宁波大学物理科学与技术学院,宁波315211 [2]浙江工业大学理学院,杭州310014

出　　处：《物理学报》2023年第10期32-41,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12235007,11975131,11435005);宁波大学王宽诚幸福基金;浙江省自然科学基金(批准号:LQ20A010009)资助的课题~~

摘　　要：可积系统研究是物理和数学等学科的重要研究课题.然而,通常的可积系统研究往往被限制在(1+1)维和(2+1)维,其原因是高维可积系统极其稀少.最近,我们发现利用形变术可以从低维可积系统导出大量的高维可积系统.本文利用形变术,将(1+1)维的Kaup-Newell(KN)系统推广到(4+1)维系统.新系统除了包含原来的(1+1)维的KN系统外,还包含三种(1+1)维KN系统的互反形式.模型也包含了许多新的(D+1)维(D≤3)的互反型可积系统.(4+1)维互反型KN系统的Lax可积性和对称可积性也被证明.新的互反型高维KN系统的求解非常困难.本文仅研究(2+1)维互反型导数非线性薛定谔方程的行波解,并给出薛定谔方程孤子解的隐函数表达式.The study of integrable systems is one of important topics both in physics and in mathematics.However,traditional studies on integrable systems are usually restricted in(1+1)and(2+1)dimensions.The main reasons come from the fact that high-dimensional integrable systems are extremely rare.Recently,we found that a large number of high dimensional integrable systems can be derived from low dimensional ones by means of a deformation algorithm.In this paper,the(1+1)dimensional Kaup-Newell(KN)system is extended to a(4+1)dimensional system with the help of the deformation algorithm.In addition to the original(1+1)dimensional KN system,the new system also contains three reciprocal forms of the(1+1)dimensional KN system.The model also contains a large number of new(D+1)dimensional(D≤3)integrable systems.The Lax integrability and symmetry integrability of the(4+1)dimensional KN system are also proved.It is very difficult to solve the new high-dimensional KN systems.In this paper,we only investigate the traveling wave solutions of a(2+1)dimensional reciprocal derivative nonlinear Schrödinger equation.The general envelope travelling wave can be expressed by a complicated elliptic integral.The single envelope dark(gray)soliton of the derivative nonlinear Schödinger equation can be implicitly written.

关 键 词：高维可积模型 Kaup-Newell系统 形变术 行波解 

分 类 号：O175[理学—数学]