Excitations of nonlinear local waves described by the sinh-Gordon equation with a variable coefficient |
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Affiliation: | 1. Department of Electronic Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300, China;2. School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China;3. Texas A & M University at Qatar, 23874 Doha, Qatar;4. Department of Medical Science, Shunde Polytechnic, Guangdong Province, Shunde 528300, China |
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Abstract: | We explore novel excitations in the form of nonlinear local waves, which are described by the sinh-Gordon (SHG) equation with a variable coefficient. With the aid of the self-similarity transformation, we establish the relationship between solutions of the SHG equation with a variable coefficient and those of the standard SHG equation. Then, using the Hirota bilinear method, we obtain a more general bilinear form for the standard SHG equation and find new one- and two-soliton waves whose forms involve two arbitrary self-similarity functions. By an appropriate choice of the smooth self-similarity functions, we determine and display novel localized waves, and discuss their properties. The method used here can be extended to the three- and higher order soliton solutions. |
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Keywords: | Solitary wave solutions Sinh-Gordon (SHG) equation The Hirota bilinear method |
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