Multiphase solutions and their reductions for a nonlocal nonlinear Schrodinger equation with focusing nonlinearity

被引:5
作者
Matsuno, Yoshimasa [1 ,2 ]
机构
[1] Yamaguchi Univ, Grad Sch Sci & Technol Innovat, Div Appl Math Sci, Ube, Yamaguchi, Japan
[2] Yamaguchi Univ, Grad Sch Sci & Technol Innovat, Div Appl Math Sci, Ube, Yamaguchi 7558611, Japan
关键词
direct method; integrability; multiphase solution; multisoliton solution; nonlocal NLS equation; MULTISOLITON SOLUTIONS; WAVES; LIMIT;
D O I
10.1111/sapm.12610
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A nonlocal nonlinear Schrodinger equation with focusing nonlinearity is considered, which has been derived as a continuum limit of the Calogero-Sutherland model in an integrable classical dynamical system. The equation is shown to stem from the compatibility conditions of a system of linear partial differential equations (PDEs), assuring its complete integrability. We construct a nonsingular N-phase solution (N: positive integer) of the equation by means of a direct method. The features of the one- and two-phase solutions are investigated in comparison with the corresponding solutions of the defocusing version of the equation. We also provide an alternative representation of the N-phase solution in terms of solutions of a system of nonlinear algebraic equations. Furthermore, the eigenvalue problem associated with the N-phase solution is discussed briefly with some exact results. Subsequently, we demonstrate that the N-soliton solution can be obtained simply by taking the long-wave limit of the N-phase solution. The similar limiting procedure gives an alternative representation of the N-soliton solution as well as the exact results related to the corresponding eigenvalue problem.
引用
收藏
页码:883 / 922
页数:40
相关论文
共 37 条
[1]   Integrable hydrodynamics of Calogero-Sutherland model: bidirectional Benjamin-Ono equation [J].
Abanov, Alexander G. ;
Bettelheim, Eldad ;
Wiegmann, Paul .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (13)
[2]   A focusing-defocusing intermediate nonlinear Schrödinger system [J].
Berntson, Bjorn K. ;
Fagerlund, Alexander .
PHYSICA D-NONLINEAR PHENOMENA, 2023, 451
[4]   MULTIPHASE SOLUTIONS OF THE BENJAMIN-ONO-EQUATION AND THEIR AVERAGING [J].
DOBROKHOTOV, SY ;
KRICHEVER, IM .
MATHEMATICAL NOTES, 1991, 49 (5-6) :583-594
[5]  
Dubrovin B. A., 1975, Funct. Anal. Appl, V9, P215, DOI 10.1007/BF01075598
[6]  
Fadeev LD., 2007, HAMILTONIAN METHODS
[7]  
G?rard P., CALOGERO MOSER DERIV
[8]  
Hirota R., 2004, Cambridge Tracts in Mathematics, DOI 10.1017/CBO9780511543043
[9]   New representations of multiperiodic and multisoliton solutions for a class of nonlocal soliton equations [J].
Matsuno, Y .
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2004, 73 (12) :3285-3293
[10]   EXACT MULTI-SOLITON SOLUTION OF THE BENJAMIN-ONO EQUATION [J].
MATSUNO, Y .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1979, 12 (04) :619-621