Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation |
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| Authors: | J L Bona W R McKinney J M Restrepo |
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| Institution: | (1) Department of Mathematics and Texas Institute for Computational and Applied Mathematics, University of Texas, Austin, TX 78712, USA %bona@math.utexas.edu , US;(2) Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA, US;(3) Mathematics Department and Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA e-mail: restrepo@math.arizona.edu, US |
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| Abstract: | Summary. Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation
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.
Received March 28, 2000; accepted August 24, 2000 %%Online publication November 15, 2000 Communicated by Thanasis Fokas |
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| Keywords: | , BBM equation, generalized BBM equation, RLW equation, generalized RLW equation, stable solitary-waves, unstable,,,,,solitary-waves |
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