Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 18, Issue 10, Pages 2667-2678Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2013.01.020
Keywords
Two-component short pulse equation; Integral bifurcation method; Two-loop soliton; Periodic two-loop wave; Periodic loop-compacton wave; Two-loop soliton with kerf of figure eight
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Funding
- Natural Science Foundation of Yunnan Province [2011FZ193]
- National Natural Science Foundation of China [11161020]
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In this paper, by using the integral bifurcation method and the Sakovich's transformations, we study the two-component short pulse equations of the first kind, different kinds of exact traveling wave solutions with two-loop character, such as two-loop soliton solutions, periodic loop-compacton wave solutions and different kinds of periodic two-loop wave solutions are obtained. Further, we discuss their dynamical behaviors of these exact traveling wave solutions and show their profiles of time evolution by illustrations. This is first time in our research area that we obtain two-soliton solutions of nonlinear partial differential equations under no help of Hirota's method, inverse scattering method, Darboux transformation and Bachlund transformation. (C) 2013 Elsevier B.V. All rights reserved.
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