Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions |
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| Authors: | Cheng-Shi Liu |
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| Affiliation: | Department of Mathematics, Northeast Petroleum University, Daqing 163318, China |
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| Abstract: | ![]()
In the paper, we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions. We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity. And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept. Our mathematical tool is the logarithmic trial equation method. |
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| Keywords: | Gaussian solitary wave Gausson logarithmic nonlinearity wave equation trial equation method |
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