JIAN-GUO LIU
Articles written in Pramana – Journal of Physics
Volume 90 Issue 6 June 2018 Article ID 0071 Research Article
Multiple periodic-soliton solutions of the (3 + 1)-dimensional generalised shallow water equation
Based on the extended variable-coefficient homogeneous balance method and two newansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of (3+1)-dimensional generalised shallowwater equations.Completely newperiodic-soliton solutions including periodic cross-kinkwave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.
Volume 94 All articles Published: 10 January 2020 Article ID 0021 Research Article
In this paper, a (2+1)-dimensional nonlinear evolution equation (NLEE), namely the generalised Camassa–Holm–Kadomtsev–Petviashvili equation (gCHKP) or Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation (KP-BBM), is examined. After applying the newly developed generalised exponential rational function method (GERFM), 14 travelling wave solutions are formally generated. It is worth mentioning that by specifying values to free parameters some previously obtained solutions can be recovered. The simplest equation method (SEM) is used to prove that the solutions obtained by GERFM are good. With the aid of a symbolic computation system, we prove that GERFM is more efficient and faster.
Volume 94, 2020
All articles
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
© 2021-2022 Indian Academy of Sciences, Bengaluru.