Journal
WAVE MOTION
Volume 79, Issue -, Pages 44-56Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.wavemoti.2018.02.009
Keywords
Nonlinear wave equation; Darboux transformation; Soliton solutions
Categories
Funding
- National Natural Science Foundation of China [11331008, 11522112]
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In this paper, a new nonlinear wave equation associated with a 2 x 2 matrix spectral problem is proposed by means of the zero-curvature equation and the polynomial expansion of the spectral parameter. With the help of a gauge transformation between the corresponding Lax pair, a Darboux transformation of the nonlinear wave equation is obtained. As an application, by taking different seed solutions and using the Darboux transformation, one can get a variety of types of exact solutions for the nonlinear wave equation, like one-soliton solution, two-soliton solution, periodic solution, and Akhmediev breather solution. (C) 2018 Elsevier B.V. All rights reserved.
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