Skip to content
Research Article Open access CC BY 4.0

The First Integrals of a Second Order Ordinary Differential Equation and Application

Yanxia Hu, Xiaofei Du

Asian Journal of Research in Computer Science · pp. 1–15 · Published 4 Jul 2019

10.9734/ajrcos/2019/v3i330095

Abstract

The first integrals of second order ordinary differential equations are considered. The necessary conditions of the existence of analytical first integrals for the equation are presented. Then, the first integrals of the equation are obtained using Lie symmetry method. The results of the first integrals are applied to certain classes of partial differential equations, the conditions of nonexistence of the traveling wave solutions of the partial differential equations are obtained, and traveling wave solutions of the equations under the certain parametric conditions are also obtained.

First integral lie symmetry traveling wave solutions partial differential equations.

References (18)

  1. 1 Handbook of Mathematical Functions [DOI]
  2. 2 THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES [DOI]
  3. 3 Integrals of nonlinear equations of evolution and solitary waves [DOI]
  4. 4 The first integral method to the two-dimensional Burgers–Korteweg–de Vries equation [DOI]
  5. 5 On non-integrability of general systems of differential equations [DOI]
  6. 6 On the complete and partial integrability of non-Hamiltonian systems [DOI]
  7. 7 Polynomial first integrals for quasi-homogeneous polynomial differential systems [DOI]
  8. 8 Integrability and symmetries for the Helmholtz oscillator with friction [DOI]
  9. 9 Exact solitary wave solution for the fractional and classical GEW-Burgers equations: an application of Kudryashov method [DOI]
  10. 10 Lie symmetry analysis and exact solutions of fractional ordinary differential equations with neutral delay [DOI]
  11. 11 An exact solution to two-dimensional Korteweg-de Vries-Burgers equation [DOI]
  12. 12 Traveling wave solutions to a reaction-diffusion equation [DOI]
  13. 13 The Completely Integrable Differential Systems are Essentially Linear Differential Systems [DOI]
  14. 14 Varieties and analytic normalizations of partially integrable systems [DOI]
  15. 15 One-parameter Lie groups and inverse integrating factors of n-th order autonomous systems [DOI]
  16. 16 Non-integrability for general nonlinear systems [DOI]
  17. 17 Local analytic first integrals of planar analytic differential systems [DOI]
  18. 18 Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation

Cited by 0

No indexed citations yet.

Related research

Article metrics

Real usage data collected on this platform.

26

Page views

0

PDF downloads

3

Outbound clicks

0

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.