TY - JOUR
T1 - Higher order corrections for shallow-water solitary waves
T2 - Elementary derivation and experiments
AU - Halász, Gábor B.
PY - 2009
Y1 - 2009
N2 - We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first-order equation is shown to be equivalent to the Korteweg-de Vries (KdV) equation, while the second-order equation is solved numerically. The propagation velocity found for the solitary waves of the second-order equation coincides with a known expression, but it is obtained in a simpler way. By measuring the propagation velocity of solitary waves in the laboratory, we demonstrate that the second-order theory gives a considerably improved fit to experimental results.
AB - We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first-order equation is shown to be equivalent to the Korteweg-de Vries (KdV) equation, while the second-order equation is solved numerically. The propagation velocity found for the solitary waves of the second-order equation coincides with a known expression, but it is obtained in a simpler way. By measuring the propagation velocity of solitary waves in the laboratory, we demonstrate that the second-order theory gives a considerably improved fit to experimental results.
UR - http://www.scopus.com/inward/record.url?scp=72449190681&partnerID=8YFLogxK
U2 - 10.1088/0143-0807/30/6/009
DO - 10.1088/0143-0807/30/6/009
M3 - Article
AN - SCOPUS:72449190681
SN - 0143-0807
VL - 30
SP - 1311
EP - 1323
JO - European Journal of Physics
JF - European Journal of Physics
IS - 6
ER -