Multiwave interaction solutions for a (3+1)-dimensional nonlinear evolution equation
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ORIGINAL PAPER
Multiwave interaction solutions for a (3+1)-dimensional nonlinear evolution equation Wenying Cui · Wei Li · Yinping Liu
Received: 29 April 2020 / Accepted: 6 July 2020 © Springer Nature B.V. 2020
Abstract In this paper, by the direct algebraic method, together with the inheritance solving strategy, new types of interaction solutions among solitons, rational waves and periodic waves are constructed for a (3+1)dimensional nonlinear evolution equation. Meanwhile, based on the simplified Hirota method, its interaction solutions among solitons, breathers and lumps of any higher orders are established by an N -soliton decomposition algorithm, together with the parameters conjugated assignment and long wave limit techniques. Finally, we demonstrate the dynamical behaviors of new interaction solutions by graphs. Keywords Simplified Hirota method · Long wave limit · Parameters conjugated assignment · Inheritance solving · Interaction solution
Y. Liu (B) School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China e-mail: [email protected] W. Cui School of Mathematical Sciences, East China Normal University, Shanghai 200241, China e-mail: [email protected] W. Li School of Computer Science and Technology, East China Normal University, Shanghai 200241, China
1 Introduction Higher dimensional nonlinear evolution equations, which closely related to physics, play an important role in the research of nonlinear science. Recently, the investigation of various wave solutions for higher dimensional nonlinear evolution equations has attracted much attention of many scholars, and new research results have been born, successively [1–7]. In this paper, we consider the (3+1)-dimensional nonlinear evolution equation (NEE) 3u x z − (2u t + u x x x − 2uu x ) y + 2(u x ∂x−1 u y )x = 0, (1) where ∂x−1 represents an inverse operator of the partial differential operator ∂x . This equation was proposed by Geng [8] in 2003 and its algebraic-geometric solutions have been obtained at the same time. Equation (1) can be decomposed into three core equations of AKNS hierarchy in different dimensions: the nonlinear Schrödinger (NLS) equation [9], the complex modified Korteweg-de Vries equation [10] and higher order NLS equation [11]. These equations were widely used in nonlinear optics, Bose-Einstein condensation, plasma physics, hydrodynamics and other fields [12,13]. Subsequently, some good results for Eq. (1) have been obtained, such as soliton solutions, breather solutions, lump solutions, rogue wave solutions, rational solutions as well as low order interaction solutions between solitons and lumps [14–21].
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At now, the symbolic computation of interaction solutions for nonlinear evolution equations has attracted much attention of many scholars. Some relevant research results have been reported [1,4,5,22]. However, the majority of the reported interaction solutions are obtained by the direct algebraic method and these interaction solutions ar
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