Nonlinear Ritz Approximation for the Camassa-Holm Equation by Using the Modify Lyapunov-Schmidt method

Authors

Hadeel G. Abd Ali, Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.Follow
Mudhir A. Abdul Hussain, Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.Follow

Abstract

In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two. The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

Keywords

Bifurcation of Solutions, Benjamin-Bona-Mahony equation, Camassa-Holm equation, Caustic, Modify Lyapunov-Schmidt method.

Article Type

Article

How to Cite this Article

Ali, Hadeel G. Abd and Abdul Hussain, Mudhir A. (2023) "Nonlinear Ritz Approximation for the Camassa-Holm Equation by Using the Modify Lyapunov-Schmidt method," Baghdad Science Journal: Vol. 20: Iss. 5, Article 2.
DOI: https://doi.org/10.21123/bsj.2023.6932