Nonlinear Ritz Approximation for the Camassa-Holm Equation by Using the Modify Lyapunov-Schmidt method
DOI:
https://doi.org/10.21123/bsj.2023.6932Keywords:
Bifurcation of Solutions, Benjamin-Bona-Mahony equation, Camassa-Holm equation, Caustic, Modify Lyapunov-Schmidt method.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.
Received 15/1/2022, Revised 7/8/2022, Accepted 8/8/2022, Published Online First 20/2/2023
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