caa a22 4500 475805283 CHVBK 20180406123745.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1007/s003320010003 doi (NATIONALLICENCE)springer-10.1007/s003320010003 Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation [Elektronische Daten] [J. L. Bona, W. R. McKinney, J. M. Restrepo] Summary. : Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation $$u_t + u_x + \alpha \left( {u^p } \right)_x - \beta u_{xxt} = 0.$$ For p>5, the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of solutions of the equation, the dynamics of suitably perturbed solitary waves are examined. Among other conclusions, we find that unstable solitary waves may evolve into several, stable solitary waves and that positive initial data need not feature solitary waves at all in its long-time asymptotics. Springer-Verlag New York Inc., 2000 Key words. BBM equation, generalized BBM equation, RLW equation, generalized RLW equation, stable solitary-waves, unstable solitary-waves nationallicence Bona J. L. Department of Mathematics and Texas Institute for Computational and Applied Mathematics, University of Texas, Austin, TX 78712, USA %bona@math.utexas.edu, US aut McKinney W. R. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA, US aut Restrepo J. M. Mathematics Department and Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA e-mail: restrepo@math.arizona.edu, US aut Journal of Nonlinear Science Springer-Verlag 10/6(2000-12-01), 603-638 0938-8974 10:6<603 2000 10 332 https://doi.org/10.1007/s003320010003 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003320010003 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bona J. L. Department of Mathematics and Texas Institute for Computational and Applied Mathematics, University of Texas, Austin, TX 78712, USA %bona@math.utexas.edu, US aut NATIONALLICENCE 700 1- McKinney W. R. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA, US aut NATIONALLICENCE 700 1- Restrepo J. M. Mathematics Department and Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA e-mail: restrepo@math.arizona.edu, US aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/6(2000-12-01), 603-638 0938-8974 10:6<603 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer