TY - JOUR
T1 - Weak solutions of a generalized Boussinesq system
AU - Li, Y. A.
PY - 1999
Y1 - 1999
N2 - We study the convergence of homoclinic orbits and heteroclinic orbits in the dynamical system governing traveling wave solutions of a perturbed Boussinesq systems modeling two-directional propagation of water waves. Nonanalytic weak solutions are found to be limits of these orbits, including compactons, peakons, and rampons, as well as infinitely many mesaons occurring at the same fixed point in the dynamical system. Singularities of solitary wave solutions in the system are also studied to understand the important impact of both linear and nonlinear dispersion terms on the regularity of these solutions.
AB - We study the convergence of homoclinic orbits and heteroclinic orbits in the dynamical system governing traveling wave solutions of a perturbed Boussinesq systems modeling two-directional propagation of water waves. Nonanalytic weak solutions are found to be limits of these orbits, including compactons, peakons, and rampons, as well as infinitely many mesaons occurring at the same fixed point in the dynamical system. Singularities of solitary wave solutions in the system are also studied to understand the important impact of both linear and nonlinear dispersion terms on the regularity of these solutions.
KW - Boussinesq systems
KW - Homoclinic orbits
KW - Traveling wave solutions
KW - Weak solutions
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U2 - 10.1023/A:1022611428785
DO - 10.1023/A:1022611428785
M3 - Article
AN - SCOPUS:0002371539
SN - 1040-7294
VL - 11
SP - 625
EP - 669
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
IS - 4
ER -