RT info:eu-repo/semantics/article
T1 Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations
A1 Bona, Jerry
A1 Durán, Ángel
A1 Mitsotakis, Dimitrios
AB Considered here are systems of partial di erential equations arisingin internal wave theory. The systems are asymptotic models describing the two-way propagation of long-crested interfacial waves in the Benjamin-Ono and theIntermediate Long-Wave regimes. Of particular interest will be solitary-wavesolutions of these systems. Several methods of numerically approximating thesesolitary waves are put forward and their performance compared. The outputof these schemes is then used to better understand some of the fundamentalproperties of these solitary waves.The spatial structure of the systems of equations is non-local, like thatof their one-dimensional, unidirectional relatives, the Benjamin-Ono and theIntermediate Long-Wave equations. As the non-local aspect is comprised ofFourier multiplier operators, this suggests the use of spectral methods for thediscretization in space. Three iterative methods are proposed and implementedfor approximating traveling-wave solutions. In addition to Newton-type andPetviashvili iterations, an interesting wrinkle on the usual Petviashvili methodis put forward which appears to o er advantages over the other two techniques.The performance of these methods is checked in several ways, including usingthe approximations they generate as initial data in time-dependent codes forobtaining solutions of the Cauchy problem.Attention is then turned to determining speed versus amplitude relations ofthese families of waves and their dependence upon parameters in the models.There are also provided comparisons between the unidirectional and bidirec-tional solitary waves. It deserves remark that while small-amplitude solitary-wave solutions of these systems are known to exist, our results suggest theamplitude restriction in the theory is arti cial.
SN 1553-5231
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/81304
UL https://uvadoc.uva.es/handle/10324/81304
LA spa
NO Discrete and Continuous Dynamical Systems- Series A, 2021, 41-1, p.87-111
DS UVaDOC
RD 13-ene-2026