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Blow-up solution near the traveling waves for the second-order Camassa–Holm equation |
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| Institution: | 1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China;2. Department of Mathematics, Nanjing Forestry University, Nanjing 310037, PR China;1. Graduate Program in Computational Modeling, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora, Brazil;2. Dep. of Mathematics, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora-MG, Brazil;1. Department of Mathematics, Indian Institute of Science, Bangalore 560012, India;2. Dipartimento di Matematica dell’Università degli Studi di Trento via Sommarive 14, 38050 Povo di Trento, Italy |
| Abstract: | This paper studies the blow-up solution and its blow-up rate near the traveling waves of the second-order Camassa–Holm equation. The sufficient condition for the existence of blow-up solution is obtained by a rather ingenious method. Applying the extended pseudo-conformal transformation, an equivalent proposition of the solution breaking in finite time near the traveling waves is constructed. The relation is established between the blow-up time and rate of the solution and the residual’s. |
| Keywords: | Second-order Camassa–Holm equation Blow-up Traveling wave Pseudo-conformal transformation |
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