PRECISE TRAVELING WAVE SOLUTIONS FOR NONLINEAR SCHRÖDINGER EQUATIONS

Amhimmid A. Alsaqa; Abdullah M. Arwiniya

doi:10.59743/jbs.v37i1.263

المؤلفون

Amhimmid A. Alsaqa Mathematics Dept., Faculty of Science, Alasmarya Islamic University, Zliten-Libya
Abdullah M. Arwiniya Mathematics Dept., Faculty of Science, Alasmarya Islamic University, Zliten-Libya

DOI:

https://doi.org/10.59743/jbs.v37i1.263

الكلمات المفتاحية:

Auxiliary equation، traveling wave، Schrödinger equations

الملخص

This paper addresses challenges associated with the study of nonlinear partial differential equations. Various methods have been utilized for the analytical resolution of these equations. In this discussion, we implement the auxiliary equation method, specifically using the auxiliary equation (φ′(ξ)) ² =aφ²(ξ)+bφ⁴(ξ)+cφ⁶(ξ), to derive the exact traveling wave solutions for two advanced nonlinear Schrödinger equations.

المراجع

L. Debnath, ''Nonlinear partial differential equations for scientists and engineers,'' Birkhauser Boston Inc., 1997, DOI 10.1007/978-0-8176-8265-1

J. D. Murray, ''Mathematical biology,'' Springer-Verlag, New York, vol. 17, pp. 551, 1993.

M. Ablowitz and P. A. Clarkson, "Solitons, nonlinear evolution equations and inverse scattering," London Mathematical Society Lecture Note Series, Cambridge: Cambridge University Press, 1991.

R. Hirota, "Exact solution of the KDV equation for multiple collisions of solitons," Physical Review Letters, vol. 27, no. 18, pp. 1192-1194, Nov. 1971.

N. A. Kudryashov, "On types of nonlinear nonintegrable equations with exact solutions," Physics Letters A, vol. 155, no. 4, pp. 269-275, May. 1991.

M.R. Miura, "Bäcklund transformation," Berlin, Springer, 1978.

B. Lu, "Bäcklund transformation of fractional riccati equation and its applications to nonlinear fractional partial differential equations," Physics Letters A, vol. 376, no. 28, pp. 2045-2048, Jun. 2012.

Y. P. Wang, "Solving the (3+1)-dimensional potential – YTSF equation with Exp-function method," Journal of Physics: Conference Series 96, no. 1, Feb. 2008, https://doi.org/10.1088/1742-6596/96/1/012186.

K. Khan, and M. A. Akbar, "Traveling wave solutions of the (2 +1)-dimensional zoomeron equation and the burgers equations via the MSE method and the Exp-Function method," Ain Shams Engineering Journal, pp. 247–256, 2013, https://doi.org/10.1016/j.asej.2013.07.007.