Theses and Dissertations - UTRGV

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Dr. Baofeng Feng

Second Advisor

Dr. Zhijun Qiao

Third Advisor

Dr. Vesselin Vatchev


We study the periodic and solitary wave solutions to several short wave model equations arising from a so-called $\beta$-family equation for $\beta=1,2,4$. These are integrable cases which possess Lax pair and multi-soliton solutions. By phase plane analysis, either the loop or cuspon type solutions are predicted. Then, by introducing a hodograph, or reciprocal, transformation, a coupled system is derived for each $\beta$. Applying a travelling wave setting, we are able to find the periodic solutions exactly expressed in terms of Jacobi Elliptic functions. In the limiting cases of modulus k=1, they all converge to the known solitary waves.


Copyright 2020 Andrey V. Stukopin. All Rights Reserved.

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