Nonlinear Dynamics

, Volume 94, Issue 4, pp 2327–2334 | Cite as

Families of nonsingular soliton solutions of a nonlocal Schrödinger–Boussinesq equation

  • Ying Shi
  • Yongshuai Zhang
  • Shuwei XuEmail author
Original Paper


Nonlocal nonlinear evolution equations with self-induced parity–time symmetric potential have received intensive attention, due to their good applications in nonlinear optics. A nonlocal Schrödinger–Boussinesq equation is proposed in this paper. By using the Hirota bilinear method and the Kadomtsev–Petviashvili hierarchy reduction method, explicit soliton solution with the nonzero boundary condition is succinctly constructed in terms of determinant. Typical dynamics and asymptotic behaviours of three types of two-soliton solutions are discussed in detail.


Nonlocal Schrödinger–Boussinesq equation Soliton Bilinear method KP hierarchy reduction 



This work is supported by the NSF of China under Grant Nos. 11501510 and 11601187.

Compliance with ethical standards

Conflict statement

We declare we have no conflict of interests.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of ScienceZhejiang University of Science and TechnologyHangzhouPeople’s Republic of China
  2. 2.College of Mathematics Physics and Information EngineeringJiaxing UniversityJiaxingPeople’s Republic of China

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