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In this study, two efficient numerical schemes based on B-spline finite element method (FEM) and time-splitting methods for solving Rosenau-KdV-RLW equation are presented. ... For the second method, after splitting Rosenau-KdV-RLW equation in time, it is solved by Strang timesplitting technique using cubic B-spline Galerkin FEM. ... In this study, the numerical solutions of Rosenau-KdV-RLW equation (2) with the initial condition is the wave profile and is linear evolution term, is advection term, is dispersion term, and are dissipative ...doi:10.48129/kjs.v48i1.8610 fatcat:nfsz5iwwfjb3zpdnfh4oj3mzoy
A generalized viscous Rosenau equation containing linear and nonlinear advective terms and mixed third- and fifth-order derivatives is studied numerically by means of an implicit second-order accurate ... method in time that treats the first-, second-, and fourth-order spatial derivatives as unknown and discretizes them by means of three-point, fourth-order accurate, compact finite differences. ... Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper. ...doi:10.1155/2016/4618364 fatcat:7pf24dvfwra47fopwvptr7rc2y
In the absence of dissipation the BBM-like equations are found to support soliton and compacton/anticompacton solutions depending on whether the dispersive term is linear or nonlinear. ... The dissipative effect is found to convert the solitons either to undular bores or to shock-like waves depending on the degree of nonlinearity of the equations. ... Acknowledgement The authors would like to thank Drs. Sk. Golam Ali and Amitava Choudhuri for their kind interest in this work. ...arXiv:1504.02825v1 fatcat:37m2hz6v4zfklbdcjoc2buytbq
This result is used to prove the decay of solutions of the evolution equations linearized about the solitary wave, in two of the models. ... With respect to a weighted norm designed to diminish as perturbations convect away from the wave profile, we prove that nonzero eigenvalues are absent in a half-plane of the form ᑬ)yb for some b) 0, for ... part of this work was completed. ...doi:10.1111/1467-9590.00063 fatcat:dtbz2adoavcmdfyeyrdwn7twzu