NEW MULTI-SOLITON SOLUTIONS OF WHITHAM-BROER-KAUP SHALLOW-WATER-WAVE EQUATIONS

作者：Zhang, Sheng^*; Liu, Mingying; Xu, Bo

来源：Thermal Science, 2017, 21(suppl. 1): S137-S144.

DOI：10.2298/TSCI17S1137Z

• Whitham-Broer-Kaup equations
• Ablowitz-Kaup-Newell-Segur equations
• Hirota's bilinear method
• Bilinear forms
• soliton solution

In this paper, new and more general Whitham-Broer-Kaup equations which can describe the propagation of shallow-water waves are exactly solved in the framework of Hirota's bilinear method and new multi-soliton solutions are obtained. To be specific, the Whitham-Broer-Kaup equations are first reduced into Ablowitz-Kaup-Newell-Segur equations. With the help of this equations, bilinear forms of the Whitham-Broer-Kaup equations are then derived. Based on the derived bilinear forms, new one-soliton solutions, two-soliton solutions, three-soliton solutions, and the uniform formulae of n-soliton solutions are finally obtained. It is shown that adopting the bilinear forms without loss of generality play a key role in obtaining these new multi-soliton solutions.

• 出版日期2017
• 单位渤海大学