caa a22 4500 606167048 CHVBK 20210128100701.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10665-014-9744-z doi (NATIONALLICENCE)springer-10.1007/s10665-014-9744-z Cho Yeunwoo Division of Ocean Systems Engineering, School of Mechanical, Aerospace and Systems Engineering, Korea Advanced Institute of Science and Technology, Daehakro 291, 305-701, Taejon, Korea aut A modified Petviashvili method using simple stabilizing factors to compute solitary waves [Elektronische Daten] [Yeunwoo Cho] A modified Petviashvili method is proposed for the computation of steady solitary-wave solutions to a nonlinear dispersive wave equation in fluids. The main difference between the Petviashvili's original method and the proposed method lies in the choice of a stabilizing factor. Compared to the original Petviashvili method, the proposed method adopts much simpler stabilizing factors such as the maximum, the $$l^{2}$$ l 2 -norm, and the central value of the intermediate relevant terms during iteration in the wavenumber domain. The motivation for using these stabilizing factors derives from the power method in the classical matrix eigenvalue problem, where the same stabilizing factors are often adopted to find the dominant eigenvector. In a similar vein, the Fourier-transformed nonlinear wave equation with power-law nonlinearity can be interpreted as a nonlinear eigenvalue problem, where the associated matrix is unknown, and can be iteratively solved by the proposed method, in which the resultant solitary-wave solution corresponds to the inverse Fourier transform of the final dominant eigenvector. Based on the proposed method, steady 2-D and 3-D solitary waves are effectively obtained for several exemplary nonlinear dispersive wave equations with power-law nonlinearities. Springer Science+Business Media Dordrecht, 2015 Dominant eigenvector nationallicence Fluids nationallicence Nonlinear wave equation nationallicence Petviashvili's method nationallicence Power-law nonlinearity nationallicence Solitary waves nationallicence Stabilizing factors nationallicence Journal of Engineering Mathematics Springer Netherlands 91/1(2015-04-01), 37-57 0022-0833 91:1<37 2015 91 10665 https://doi.org/10.1007/s10665-014-9744-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9744-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cho Yeunwoo Division of Ocean Systems Engineering, School of Mechanical, Aerospace and Systems Engineering, Korea Advanced Institute of Science and Technology, Daehakro 291, 305-701, Taejon, Korea aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 91/1(2015-04-01), 37-57 0022-0833 91:1<37 2015 91 10665