Classification of single-wave and bi-wave motion through fourth-order equations generated from the Ito model

Abstract

Recently, two fourth-order integrable equations were established by Wazwaz using the Boussinesq model. Tian and Zhang subsequently demonstrated that both equations are potential forms of the Ito model. This study investigates the dynamics of these equations using three effective schemes: the modified rational sine-cosine functions, Kudryashov-expansion, and the Hirota bilinear forms. The study reports novel findings, including the observation that although these equations were derived from the same model, one propagates as a single-wave while the other propagates as a bi-wave. Additionally, some solutions of one equation can be obtained from the solutions of the other equation. These results are expected to be highly significant in the study of propagation solitary wave-solutions for nonlinear equations.

Necessary conditions for convex-periodic, elliptic-periodic, inclined-periodic, and rogue wave-solutions to exist for the multi-dispersions Schrodinger equation

“…Here, we implement three effective schemes to investigate possible complex solutions to the proposed Schrodinger model. We use the extended tanh-coth method [21][22][23], rational sine-cosine functions, and rational sinh-cosh functions [20,24,25].…”

Optical Solitons for the Dispersive Concatenation Model: Undetermined Coefficients

“…Later during 2015, this model was extended with a dispersive component added to it and is being referred to as the dispersive concatenation model [3][4][5]. The physical application of the proposed model is to study the dynamics of solitons that propagate through single-mode fibers across trans-oceanic and trans-continental distances [26][27][28][29][30][31][32][33][34].…”

“…However, the resulting the parameter A is ( ) Here, the resulting parameter B is the same as the case for bright soliton (20) along with corresponding constraints. Therefore, the type-I singular soliton solution for the considered concatenation system resulted to be where the parameter A is given in (31), while the wave number and the parameter B are the same as in bright 1-soliton given on ( 17) and ( 20) respectively, along with their corresponding solvability constraints.…”