SOLUTIONS OF THE KORTEWEG-DEVRIES EQUATION

被引:30
作者
ABLOWITZ, MJ [1 ]
CORNILLE, H [1 ]
机构
[1] CENS,F-91190 GIF SUR YVETTE,FRANCE
关键词
D O I
10.1016/0375-9601(79)90467-5
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A method to construct solutions decaying like 2 x2, as |x| → ∞, to the Korteweg-de Vries equation, and its higher-order analogues is given. Solutions to the higher KdV equations, decaying like l(l + 1) x2 can also be constructed. Similar ideas apply to the other nonlinear evolution equations and we give brief results concerning the modified Korteweg-de Vries equation. © 1979.
引用
收藏
页码:277 / 280
页数:4
相关论文
共 12 条
[1]   SOLITONS AND RATIONAL SOLUTIONS OF NON-LINEAR EVOLUTION EQUATIONS [J].
ABLOWITZ, MJ ;
SATSUMA, J .
JOURNAL OF MATHEMATICAL PHYSICS, 1978, 19 (10) :2180-2186
[2]  
AIRAULT H, 1977, COMMUN PUR APPL MATH, V30, P1
[3]  
BLAZEK M, 1966, COMMUN MATH PHYS, V3, P282
[4]   DIFFERENTIAL EQUATIONS SATISFIED BY FREDHOLM DETERMINANTS AND APPLICATION TO INVERSION FORMALISM FOR PARAMETER DEPENDENT POTENTIALS [J].
CORNILLE, H .
JOURNAL OF MATHEMATICAL PHYSICS, 1976, 17 (12) :2143-2158
[5]   GENERALIZATION OF INVERSION EQUATIONS AND APPLICATION TO NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS .1. [J].
CORNILLE, H .
JOURNAL OF MATHEMATICAL PHYSICS, 1977, 18 (09) :1855-1869
[7]   SOME GENERAL RESULTS FOR INVERSE-SCATTERING THEORY AT FIXED ANGULAR-MOMENTUM OR AT FIXED ENERGY [J].
CORNILLE, H .
NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA A-NUCLEI PARTICLES AND FIELDS, 1973, A 14 (01) :141-160
[8]   THRESHOLD-BEHAVIOR REQUIREMENTS FOR P-WAVE N/D EQUATIONS [J].
CORNILLE, H ;
RUBINSTEIN, G .
JOURNAL OF MATHEMATICAL PHYSICS, 1968, 9 (09) :1501-+
[9]   N/D EQUATIONS - SELF-DAMPING MECHANISM THRESHOLD BEHAVIOUR AND SUBTRACTED EQUATIONS REGGE-POLE HYPOTHESIS [J].
CORNILLE, H ;
RUBINSTEIN, G .
NUOVO CIMENTO A, 1968, 56 (04) :867-+
[10]   KORTEWEG-DEVRIES EQUATION AND GENERALIZATIONS .6. METHODS FOR EXACT SOLUTION [J].
GARDNER, CS ;
GREENE, JM ;
KRUSKAL, MD ;
MIURA, RM .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1974, 27 (01) :97-133