• JIAN-GUO LIU

      Articles written in Pramana – Journal of Physics

    • Multiple periodic-soliton solutions of the (3 + 1)-dimensional generalised shallow water equation

      YE-ZHOU LI JIAN-GUO LIU

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      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.

    • Exact solitary wave solutions to the (2 + 1)-dimensional generalised Camassa–Holm–Kadomtsev–Petviashvili equation

      BEHZAD GHANBARI JIAN-GUO LIU

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      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.

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