Exact periodic cross-kink wave solutions and breather type of two-solitary wave solutions for the (3 + 1)-dimensional potential-YTSF equation

Novel dynamical behaviors of interaction solutions of the new (3+1)-dimensional integrable fourth-order nonlinear equation

“…Recently, the interaction solutions among the lump waves, rouge waves and other solitary waves of NLPDEs have attracted the attention of many scholars. Various powerful methods have been proposed to construct these solutions of NLPDEs, such as the inverse scattering transformation (Ablowitz and Clarkson 1991), the Darboux transformation method (Imai and Nozaki 1996;Wang et al 2015), Hirota's bilinear method (Hirota 2004;Xu and Deng 2016;Zhou et al 2019), the quadratic function method (Ma 2015;Tan et al 2020;Ma 2016;Kaur and Wazwaz 2019;Liu and Sun 2018;Tan 2018), the extended homoclinic test approach (Li and Dai 2011;Liu 2021;), the long-wave limit method ) and other methods (Seadawy and Tariq 2021;Liu 2018;Kaur and Wazwaz 2018).…”

Periodic oscillating solitons and homoclinic breather-wave solution for the (3+1)-dimensional Jimbo-Miwa equation

“…Multi-soliton or solitary wave solutions of non-linear PDE may well describe various phenomena in physics and other fields [3][4][5][6]. Some oscillating solitons may be considered as a kind of non-propagation solitons [7][8][9][10]. To find new explicit solutions, some effective methods have been proposed [11][12][13][14][15] and the study of non-linear localized waves and interaction solutions among them is one of the important hot topics in recent years.…”

Multidromion Soliton and Rouge Wave for the (2 + 1)-Dimensional Broer-Kaup System with Variable Coefficients

“…Searching for explicit solutions of nonlinear evolution equations by using various different methods is useful and meaningful in physical science and nonlinear science. Many powerful methods have been presented, such as inverse scattering transform [1], Hirota's bilinear form method [2], two-soliton method [3], homoclinic test technique [4][5][6], the Bäcklund transformation method [7], three-wave type of ansätz approach [8,9], projective equation method [10], and multilinear variable separation method [11].…”