A CONNECTION BETWEEN NON-LINEAR EVOLUTION-EQUATIONS AND ORDINARY DIFFERENTIAL-EQUATIONS OF P-TYPE .1.

被引:818
作者
ABLOWITZ, MJ
RAMANI, A
SEGUR, H
机构
[1] PRINCETON UNIV,PROGRAM APPL MATH,PRINCETON,NJ 08540
[2] AERONAUT RES ASSOCIATES PRINCETON INC,PRINCETON,NJ 08540
关键词
D O I
10.1063/1.524491
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We develop here two aspects of the connection between nonlinear partial differential equations solvable by inverse scattering transforms and nonlinear ordinary differential equations (ODE) of P-type (i.e., no movable critical points). The first is a proof that no solution of an ODE, obtained by solving a linear integral equation of a certain kind, can have any movable critical points. The second is an algorithm to test whether a given ODE satisfies necessary conditions to be of P-type. Often, the algorithm can be used to test whether or not a given nonlinear evolution equation may be completely integrable. © 1980 American Institute of Physics.
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页码:715 / 721
页数:7
相关论文
共 11 条
[1]   NON-LINEAR EVOLUTION EQUATIONS AND ORDINARY DIFFERENTIAL-EQUATIONS OF PAINLEVE TYPE [J].
ABLOWITZ, MJ ;
RAMANI, A ;
SEGUR, H .
LETTERE AL NUOVO CIMENTO, 1978, 23 (09) :333-338
[2]   EXACT LINEARIZATION OF A PAINLEVE TRANSCENDENT [J].
ABLOWITZ, MJ ;
SEGUR, H .
PHYSICAL REVIEW LETTERS, 1977, 38 (20) :1103-1106
[3]  
ABLOWITZ MJ, UNPUBLISHED
[4]   GENERALIZATION OF INVERSION EQUATIONS AND APPLICATION TO NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS .1. [J].
CORNILLE, H .
JOURNAL OF MATHEMATICAL PHYSICS, 1977, 18 (09) :1855-1869
[5]  
GOLUBEV VV, 1953, LECTURES INTEGRALS E
[6]  
Ince E. L., 1944, ORDINARY DIFFERENTIA, pviii+558
[8]  
NAKACH R, 1977, 2 CHALM U TECHN SCH
[9]  
POGORZELSKI W, 1966, INTEGRAL EQUATIONS T, V1