Far East Journal of Mathematical Sciences (FJMS)

The Far East Journal of Mathematical Sciences (FJMS) publishes original research papers and survey articles in pure and applied mathematics, statistics, mathematical physics, and other related fields. It welcomes application-oriented work as well.

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EXACT SOLUTIONS FOR (2 + 1)-DIMENSIONAL COS-GORDON NONLINEAR PARTIAL DIFFERENTIAL EQUATION USING JACOBI ELLIPTIC FUNCTIONS

Authors

  • G. Sibisakkaravarthy
  • R. Asokan
  • T. Sankili
  • P. Harsha
  • M. Vinoth

Keywords:

travelling wave, Jacobi elliptic functions, sin-Gordon equation, exact solutions

DOI:

https://doi.org/10.17654/0972087126001

Abstract

A (2+1)-dimensional Cos-Gordon nonlinear partial differential equation is taken in this manuscript to find new exact solutions. Since we use limited expansion in this equation, this equation may be expanded to higher level to get varied solutions. A rational ansatz form is assumed to derive all possible solutions of our equation.

Received: July 22, 2025
Revised: August 28, 2025
Accepted: September 10, 2025

References

[1] S. Sirendaoreji and S. Sun Jiong, A direct method for solving sinh-Gordon type equation, Phys. Lett. A 298 (2002), 133-139.

[2] G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York, 1999.

[3] A. M. Wazwaz, Travelling wave solutions for combined and double combined sine-cosine-Gordon equations by the variable separated ODE method, Applied Mathematics and Computation 177 (2006), 755-760.

[4] P. Kaliappan and M. Lakshmanan, Kadomstev-Petviashvile and two-dimensional sine-Gordon equations: reduction to Painleve transcendents, J. Phys. A: Math. Gen. 12 (1979), 10.

[5] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys. 60(7) (1992), 650-654.

[6] Y. H. Liu, R. Guo and J. W. Zhang, Inverse scattering transform for the discrete nonlocal PT symmetric nonlinear Schrödinger equation with nonzero boundary conditions, Physica D 472 (2025), 134528.

[7] A. M. Wazwaz, A sine-cosine method for handling nonlinear wave equations, Mathematical and Computer Modelling 40 (2004), 499-508.

[8] Subin. P. Joseph, New traveling wave exact solutions to the coupled Klein-Gordon system of equations, Partial Differential Equations in Applied Mathematics 5 (2022), 100208.

[9] A. Polyanin and V. F. Zaitsev, Handbook of Ordinary Differential Equations, CRC Press Taylor and Francis Group, 2018.

Published

2025-10-04

Issue

Section

Articles

How to Cite

EXACT SOLUTIONS FOR (2 + 1)-DIMENSIONAL COS-GORDON NONLINEAR PARTIAL DIFFERENTIAL EQUATION USING JACOBI ELLIPTIC FUNCTIONS. (2025). Far East Journal of Mathematical Sciences (FJMS), 143(1), 1-9. https://doi.org/10.17654/0972087126001

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