R. Grimshaw et al., SOLITARY WAVES WITH DAMPED OSCILLATORY TAILS - AN ANALYSIS OF THE 5TH-ORDER KORTEWEG-DEVRIES EQUATION, Physica. D, 77(4), 1994, pp. 473-485
We construct oscillatory solitary wave solutions of a fifth-order Kort
eweg-de Vries equation, where the oscillations decay at infinity. Thes
e waves arise as a bifurcation from the linear dispersion curve at tha
t wavenumber where the linear phase speed and group velocity coincide.
Our approach is a wave-packet analysis about this wavenumber which le
ads in the first instance to a higher-order nonlinear Schrodinger equa
tion, from which we then obtain the steady solitary wave solution. We
then describe a complementary normal-form analysis which leads to the
same result. In addition we derive the nonlinear Schrodinger equation
for all wavenumbers, and list all the various anomalous cases.