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  1. No Access

    Article

    Novel evolutionary behaviors of localized wave solutions and bilinear auto-Bäcklund transformations for the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation

    Water waves are common phenomena in nature, which have attracted extensive attention of researchers. In the present paper, we first deduce five kinds of bilinear auto-Bäcklund transformations of the generalize...

    Peng-Fei Han, Yi Zhang, Chi-Hui ** in Nonlinear Dynamics (2023)

  2. No Access

    Article

    Dynamical behavior of multiwave interaction solutions for the (3+1)-dimensional Kadomtsev-Petviashvili-Bogoyavlensky-Konopelchenko equation

    The (3+1)-dimensional Kadomtsev-Petviashvili-Bogoyavlensky-Konopelchenko equation is used to simulate the evolution of shallow water waves with weakly nonlinear restorative forces and waves in a strong magneti...

    Peng-Fei Han, Taogetusang Bao in Nonlinear Dynamics (2023)

  3. No Access

    Article

    Bilinear auto-B \({{\ddot{\mathrm{a}}}}\) cklund transformations and higher-order breather solutions for the (3+1)-dimensional generalized KdV-type equation

    The (3+1)-dimensional generalized KdV-type equation has been found to model many physical, mechanical and engineering phenomena, including geophysical fluid dynamics, ocean engineering and plasma physics. Usin...

    Peng-Fei Han, Taogetusang Bao in Nonlinear Dynamics (2022)

  4. No Access

    Article

    Linear superposition formula of solutions for the extended (3+1)-dimensional shallow water wave equation

    Active researches on the water waves have been done, and water waves are essentially complex waves controlled by gravity field and surface tension. Using the Hirota bilinear method, two bilinear auto-Bäcklund ...

    Peng-Fei Han, Yi Zhang in Nonlinear Dynamics (2022)

  5. No Access

    Article

    Hybrid localized wave solutions for a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma

    Based on the long wave limit method and complex conjugate condition technique, we investigate hybrid localized wave solutions with different forms for the generalized Calogero–Bogoyavlenskii–Konopelchenko–Schi...

    Peng-Fei Han, Taogetusang Bao in Nonlinear Dynamics (2022)

  6. No Access

    Article

    Novel hybrid-type solutions for the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients

    In this article, the bilinear form, Bäcklund transformation, Lax pair and infinite conservation laws of the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients a...

    Peng-Fei Han, Taogetusang Bao in Nonlinear Dynamics (2022)

  7. No Access

    Article

    Interaction of multiple superposition solutions for the \((4 + 1)\) -dimensional Boiti-LeonManna-Pempinelli equation

    Water wave is one of the most common phenomena in nature, and its involves mathematical modeling, aerodynamics, computer simulation, mechanical manufacturing, marine science and so on. Hence, the water wave dy...

    Peng-Fei Han, Taogetusang Bao in Nonlinear Dynamics (2021)

  8. No Access

    Article

    Construction of abundant solutions for two kinds of \(\mathbf {(3\varvec{+}1)}\) -dimensional equations with time-dependent coefficients

    Variable-coefficient nonlinear evolution equations offer us with more real aspects in the inhomogeneities of media and non-uniformities of boundaries than their constant coefficients in some real-world problem...

    Peng-Fei Han, Taogetusang Bao in Nonlinear Dynamics (2021)