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| Breather, Soliton and Rational Solutions for the (2+1)-Dimensional Hirota Equation |
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Citation： |
Gui MU,Zhenyun QIN,Zhiqiang YANG.Breather, Soliton and Rational Solutions for the (2+1)-Dimensional Hirota Equation[J].Chinese Annals of Mathematics B,2026,(1):1~22 |
| Page view： 190
Net amount： 95 |
Authors： |
Gui MU; Zhenyun QIN;Zhiqiang YANG |
Foundation： |
National Natural Science Foundation of China (Nos. 12171098, 12261053, 11571079, 11701322) and the Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University) |
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| Abstract： |
By virtue of Hirota’s bilinear method and Kadomtsev–Petviashvili hierarchy reduction technique, the general breather, soliton and rational solutions in the (2+1)-dimensional Hirota equation are constructed. These solutions are expressed in terms of Gram determinants and Schur polynomials. The dynamics of these solutions are analyzed in detail. In particular, the interaction between lumps and breathers is discussed, which reveals that the lump can be regarded as a special limit of the breather. Moreover, the semi-rational solutions consisting of lumps, breathers and solitons are also derived, which exhibit rich wave structures. The results provide a deeper understanding of the integrable properties and nonlinear wave phenomena in higher-dimensional systems. |
Keywords： |
Hirota’s bilinear method Kadomtsev-Petviashvili hierarchy reduction technique (2+1)-Dimensional Hirota equation |
Classification： |
37K40, 35Q53 |
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