Nonlinear differential equations with exact solutions expressed via the Weierstrass function

被引：17
|
作者：
Kudryashov, NA [1 ]
机构：
[1] State Univ, Moscow Engn & Phys Inst, Dept Appl Math, Moscow 115409, Russia
来源：
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 2004年 / 59卷 / 7-8期
基金：
俄罗斯基础研究基金会;
关键词：
nonlinear differential equation; exact solution; Weierstrass function; nonlinear evolution equation;
D O I：
10.1515/zna-2004-7-807
中图分类号：
O64 [物理化学（理论化学）、化学物理学];
学科分类号：
070304 ; 081704 ;
摘要：
A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution of the simplest integrable equation. We use the Weierstrass elliptic equation as building block to find a number of nonlinear differential equations with exact solutions. Nonlinear differential equations of the second, third and fourth order with special solutions-expressed via the Weierstrass function are given.
引用
收藏
页码：443 / 454
页数：12
相关论文
共 50 条
  • [31] System of Partial Differential Equations and Analytical Representations of the Weierstrass Sigma Function
    M. M. Alekseev
    S. I. Bezrodnykh
    Mathematical Notes, 2023, 114 : 1094 - 1102
  • [32] The subsidiary ordinary differential equations and the exact solutions of the higher order dispersive nonlinear Schrodinger equation
    Zhang, Jin-Liang
    Wang, Ming-Liang
    Li, Xiang-Zheng
    PHYSICS LETTERS A, 2006, 357 (03) : 188 - 195
  • [33] Exact Solutions of Nonlinear Partial Differential Equations Using the Extended Kudryashov Method and Some Properties
    Zhou, Jian
    Ju, Long
    Zhao, Shiyin
    Zhang, Yufeng
    SYMMETRY-BASEL, 2023, 15 (12):
  • [34] EXACT SOLUTIONS OF TWO CLASSES OF SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH THE CONTACT STRUCTURE
    Wang, Kaizhi
    Zhong, Tingyu
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2025,
  • [35] On reducing and finding solutions of nonlinear evolutionary equations via generalized symmetry of ordinary differential equations
    Tsyfra, Ivan
    Rzeszut, Wojciech
    MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2022, 19 (07) : 6962 - 6984
  • [36] Logistic function as solution of many nonlinear differential equations
    Kudryashov, Nikolay A.
    APPLIED MATHEMATICAL MODELLING, 2015, 39 (18) : 5733 - 5742
  • [37] Generalized separation of variables and exact solutions of nonlinear equations
    A. F. Barannyk
    T. A. Barannyk
    I. I. Yuryk
    Ukrainian Mathematical Journal, 2011, 62 : 1852 - 1865
  • [38] Exact solutions of differential equations with delay for dissipative systems
    Hasebe, K
    Nakayama, A
    Sugiyama, Y
    PHYSICS LETTERS A, 1999, 259 (02) : 135 - 139
  • [39] EXACT SOLUTIONS FOR THE DIFFERENTIAL EQUATIONS IN FRACTAL HEAT TRANSFER
    Yang, Chun-Yu
    Zhang, Yu-Dong
    Yang, Xiao-Jun
    THERMAL SCIENCE, 2016, 20 : S747 - S750
  • [40] Exact solutions of nonlocal nonlinear field equations in cosmology
    S. Yu. Vernov
    Theoretical and Mathematical Physics, 2011, 166 : 392 - 402
12345