Exact conditions for existence of homoclinic orbits in the fifth-order KdV model
Abbreviated Journal Title
DIFFERENTIAL-EQUATIONS; WATER-WAVES; ORDERS; ASYMPTOTICS; SOLITONS; Mathematics, Applied; Physics, Mathematical
We consider homoclinic orbits in the fourth-order equation v((iv)) + (1- epsilon(2)) v" - epsilon(2)v = v(2) + gamma(2vv" + v'(2)), where (gamma, epsilon) is an element of R-2. Numerical computations [CG97, C01] show that homoclinic orbits exist on certain curves gamma(epsilon) in the parameter plane (gamma, epsilon). We study the dependence. (gamma e) in the limit e -> 0 and prove that a curve gamma(epsilon) passes through the point (gamma(0), 0) only if s(gamma(0)) = 0, where s(gamma) denotes the Stokes constant for the truncated equation (with e = 0). The additional condition s'(gamma(0)) not equal 0 guarantees the existence of a unique curve. (e) passing through the point (gamma(0), 0). Every homoclinic orbit is proved to be single- humped for sufficiently small epsilon.
"Exact conditions for existence of homoclinic orbits in the fifth-order KdV model" (2006). Faculty Bibliography 2000s. 6653.