Abstract
Via a special Painlevé–Bäcklund transformation and the linear superposition theorem, we derive the general variable separation solution of the (2 + 1)-dimensional generalized Broer–Kaup system. Based on the general variable separation solution and choosing some suitable variable separated functions, new types of V-shaped and A-shaped solitary wave fusion and Y-shaped solitary wave fission phenomena are reported.
Highlights
Modern soliton theory is widely applied in many natural science such as chemistry, biology, mathematics, communication and in almost all branches of physics like the fluid dynamics, plasma physics, field theory, nonlinear optics and condensed matter physics, and so on
Lacking theoretical and experiments related to the generalized Broer– Kaup (GBK) system, we could not further www.mii.lt/NA
We hope that in future experimental studies on these soliton fusion and fission phenomena can be realized in some fields
Summary
Modern soliton theory is widely applied in many natural science such as chemistry, biology, mathematics, communication and in almost all branches of physics like the fluid dynamics, plasma physics, field theory, nonlinear optics and condensed matter physics, and so on. Liu been successfully generalized to obtain variable separation solutions for many (1+1)-dimensional, (2 + 1)-dimensional and (3 + 1)-dimensional models. To the best of our knowledge, the studies on the general solution with arbitrary number of variable separated functions, and especially on solitons with fusion and fission properties were not reported for the (2 + 1)-dimensional generalized Broer– Kaup (GBK) system [27,28,29]. W0, P0 and Q can be derived by solving (10) and (11), respectively, while the function P is considered as arbitrary function of {x, t} We obtain another special exact excitation [a0. Even in some special cases, W0 = P0 = bi = 0, this is still very interesting for the exact variable solutions of the HBK system.
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