Huygens' principle in Minkowski spaces and soliton solutions of the Korteweg-de Vries equation

被引:33
作者
Berest, YY [1 ]
Loutsenko, IM
机构
[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
[2] Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada
关键词
D O I
10.1007/s002200050235
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A new class of linear second order hyperbolic partial differential operators satisfying Huygens' principle in Minkowski spaces is presented. The construction reveals a direct connection between Huygens' principle and the theory of solitary wave solutions of the Korteweg-de Vries equation.
引用
收藏
页码:113 / 132
页数:20
相关论文
共 42 条
[1]  
Ablowitz M.J., 1991, SOLITONS NONLINEAR E
[2]   CLASS OF POLYNOMIALS CONNECTED WITH KORTEWEG-DEVRIES EQUATION [J].
ADLER, M ;
MOSER, J .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1978, 61 (01) :1-30
[3]   RATIONAL AND ELLIPTIC SOLUTIONS OF KORTEWEG DE-VRIES EQUATION AND A RELATED MANY-BODY PROBLEM [J].
AIRAULT, H ;
MCKEAN, HP ;
MOSER, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1977, 30 (01) :95-148
[4]  
[Anonymous], COMPTES RENDUS ACAD
[5]   Lacunae of hyperbolic Riesz kernels and commutative rings of partial differential operators [J].
Berest, Y .
LETTERS IN MATHEMATICAL PHYSICS, 1997, 41 (03) :227-235
[6]   FUNDAMENTAL-SOLUTIONS FOR PARTIAL-DIFFERENTIAL EQUATIONS WITH REFLECTION GROUP INVARIANCE [J].
BEREST, Y ;
MOLCHANOV, Y .
JOURNAL OF MATHEMATICAL PHYSICS, 1995, 36 (08) :4324-4339
[7]   HUYGENS PRINCIPLE AND INTEGRABILITY [J].
BEREST, YY ;
VESELOV, AP .
RUSSIAN MATHEMATICAL SURVEYS, 1994, 49 (06) :5-77
[8]   HADAMARD PROBLEM AND COXETER GROUPS - NEW EXAMPLES OF HUYGENS EQUATIONS [J].
BEREST, YY ;
VESELOV, AP .
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1994, 28 (01) :3-12
[9]  
BEREST YY, 1993, USP MAT NAUK, V48, P181
[10]  
BEREST YY, 1997, COMMUN PURE APPL MAT, V50, P1021