Elliptic solutions for higher order KdV equations

被引：4

作者：

Hayashi, Masahito ^{[1
]}

Shigemoto, Kazuyasu ^{[2
]}

Tsukioka, Takuya ^{[3
]}

机构：

[1] Osaka Inst Technol, Osaka 5358585, Japan

[2] Tezukayama Gakuin Univ, Nara 6318501, Japan

[3] Bukkyo Univ, Kyoto 6038301, Japan

来源：

JOURNAL OF PHYSICS COMMUNICATIONS | 2020年 / 4卷 / 04期

关键词：

soliton system; Backlund transformation; KdV equation; Eliptic solution; Hyperbolic solution; Trigonometric solution; DE-VRIES EQUATION; BACKLUND TRANSFORMATION; SHALLOW-WATER; MULTIPLE COLLISIONS; WAVES; OPERATORS; EVOLUTION; SPECTRUM; COLD;

D O I：

10.1088/2399-6528/ab88df

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study higher order KdV equations from the GL(2, R) congruent to SO(2,1) Lie group point of view. We find elliptic solutions of higher order KdV equations up to the ninth order. We argue that the main structure of the trigonometric/hyperbolic/elliptic N-soliton solutions for higher order KdV equations is the same as that of the original KdV equation. Pointing out that the difference is only the time dependence, we find N-soliton solutions of higher order KdV equations can be constructed from those of the original KdV equation by properly replacing the time-dependence. We discuss that there always exist elliptic solutions for all higher order KdV equations.

引用

页数：11

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