Quasiperiodic waves and asymptotic behavior for the nonisospectral and variable-coefficient KdV equation

被引：0

作者：

Zhang, Yi ^{[1
]}

Jin, Rongjie ^{[1
]}

Dong, Kanghui ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

来源：

NONLINEAR AND MODERN MATHEMATICAL PHYSICS | 2013年 / 1562卷

关键词：

nvcKdV equation; Hirota bilinear method; Riemann theta function; Periodic wave solutions; Soliton solutions; NONLINEAR SCHRODINGER MODEL; N-SOLITON SOLUTION; DE-VRIES EQUATION; BACKLUND TRANSFORMATION; SYMBOLIC COMPUTATION; BOUSSINESQ EQUATION; EVOLUTION-EQUATIONS; BILINEAR EQUATIONS; GRAMMIAN SOLUTIONS; OPTICAL-FIBERS;

D O I：

10.1063/1.4828698

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

In this paper, quasiperiodic waves and asymptotic behavior for the nonisospectral and variable-coefficient KdV (nvcKdV) equation are considered. The Hirota bilinear method is extended to explicitly construct multiperiodic (quasiperiodic) wave solutions for the nvcKdV equation. And a limiting procedure is presented to analyze asymptotic behavior of the one-and two-periodic waves in details. The exact relations between the periodic wave solutions and the well-known soliton solutions are established. It is rigorously shown that the periodic wave solutions tend to the soliton solutions under a small amplitude limit.

引用

页码：257 / 264

页数：8

共 29 条

[1]

Ablowitz M.J., 1991, Nonlinear Evolution Equations and Inverse Scattering

[2] NONPROPAGATING SOLITONS OF THE VARIABLE-COEFFICIENT AND NONISOSPECTRAL KORTEWEG-DEVRIES EQUATION [J].

CHAN, WL ;

LI, KS .

JOURNAL OF MATHEMATICAL PHYSICS, 1989, 30 (11) :2521-2527

[3]

Fan E. G., 2009, J PHYS A, V42

[4]

Fan EG, 1998, APPL MATH MECH-ENGL, V19, P713

[5] The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials [J].

Fan, Engui .

PHYSICS LETTERS A, 2011, 375 (03) :493-497

[6] On the periodic solutions for both nonlinear differential and difference equations: A unified approach [J].

Fan, Engui ;

Chow, Kwok Wing .

PHYSICS LETTERS A, 2010, 374 (35) :3629-3634

[7] BILINEARIZATION OF SOLITON-EQUATIONS [J].

HIROTA, R .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1982, 51 (01) :323-331

[8] A vector potential KdV equation and vector Ito equation: soliton solutions, bilinear Backlund transformations and Lax pairs [J].

Hirota, R ;

Hu, XB ;

Tang, XY .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 288 (01) :326-348

[9]

Hirota R., 2004, DIRECT METHODS SOLIT

[10] Lax pair, Backlund transformation and N-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation [J].

Li, Juan ;

Xu, Tao ;

Meng, Xiang-Hua ;

Zhang, Ya-Xing ;

Zhang, Hai-Qiang ;

Tian, Bo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 336 (02) :1443-1455

← 1 2 3 →