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


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



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



          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.


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