PROPERTIES OF CONSERVATION-LAWS OF NONLINEAR EVOLUTION-EQUATIONS

被引：12

作者：

MATSUNO, Y

机构：

[1] Department of Physics, Faculty of Liberal Arts, Yamaguchi University

来源：

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN | 1990年 / 59卷 / 09期

关键词：

Bäcklund transformation; conservation law; nonlinear evolution equation; soliton;

D O I：

10.1143/JPSJ.59.3093

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A systematic method is developed for evaluating conservation laws of nonlinear evolution equations (NEE's) by employing the time parts of the Bäcklund transformations. The properties of conservation laws are then investigated in detail to obtain the informations about the structure of NEE's themselves. In particular, we focus our attention on the independence of conservation laws. The NEE's considered in this paper are the Boussinesq equation, a model equation for shallow-water waves due to Hirota and Satsuma, the Sawada-Kotera and the Kaup equations and the Ito equation. For all these equations, the inverse scattering transform problems have not been fully solved since the associated isospectral equations become higher-order ones in comparison with the usual Schrödinger equation. © 1990, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

引用

页码：3093 / 3100

页数：8

共 12 条

[1] NEW HIERARCHY OF KORTEWEG-DEVRIES EQUATIONS
CAUDREY, PJ
DODD, RK
GIBBON, JD
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1976, 351 (1666) : 407 - 422
[2] Cheng H. X., 1982, J PHYS A, V15, P3367
[3] N-SOLITON SOLUTIONS OF MODEL EQUATIONS FOR SHALLOW-WATER WAVES
HIROTA, R
SATSUMA, J
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1976, 40 (02) : 611 - 612
[4] Hirota R., 1980, Solitons, P157, DOI 10.1007/978-3-642-81448-8_5
[5] AN EXTENSION OF NON-LINEAR EVOLUTION-EQUATIONS OF THE K-DV (MK-DV) TYPE TO HIGHER ORDERS
ITO, M
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1980, 49 (02) : 771 - 778
[6] KAUP DJ, 1980, STUD APPL MATH, V62, P189
[7] NUMBER DENSITY-FUNCTION OF BENJAMIN ONO SOLITONS
MATSUNO, Y
[J]. PHYSICS LETTERS A, 1981, 87 (1-2) : 15 - 17
[8] SOLITON AND ALGEBRAIC EQUATION
MATSUNO, Y
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1982, 51 (10) : 3375 - 3380
[9] BACKLUND TRANSFORMATION FOR A HIGHER-ORDER KORTEWEG-DEVRIES EQUATION
SATSUMA, J
KAUP, DJ
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1977, 43 (02) : 692 - 697
[10] METHOD FOR FINDING N-SOLITON SOLUTIONS OF KDV EQUATION AND KDV LIKE EQUATION
SAWADA, K
KOTERA, T
[J]. PROGRESS OF THEORETICAL PHYSICS, 1974, 51 (05): : 1355 - 1367

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