Exact conditions for existence of homoclinic orbits in the fifth-order KdV model

Alexander Tovbis, Dmitry Pelinovsky
2006 Nonlinearity  
We consider homoclinic orbits in the fourth-order equation CG97, C01] show that homoclinic orbits exist on certain curves γ (ε) in the parameter plane (γ , ε). We study the dependence γ (ε) in the limit ε → 0 and prove that a curve γ (ε) passes through the point (γ 0 , 0) only if s(γ 0 ) = 0, where s(γ ) denotes the Stokes constant for the truncated equation (with ε = 0). The additional condition s (γ 0 ) = 0 guarantees the existence of a unique curve γ (ε) passing through the point (γ 0 , 0).
more » ... e point (γ 0 , 0). Every homoclinic orbit is proved to be single-humped for sufficiently small ε.
doi:10.1088/0951-7715/19/10/003 fatcat:yst6254irzcrlfb4hk2ub7ywwa