A study of resonance Y-type multi-soliton solutions and soliton molecules for new (2+1)-dimensional nonlinear wave equations

Abstract

<abstract> <p>In this study, a fourth-order nonlinear wave equation with variable coefficients was investigated. Through appropriate choice of the free parameters and using the simplified linear superposition principle (LSP) and velocity resonance (VR), the examined equation can be considered as Hirota–Satsuma–Ito, Calogero–Bogoyavlenskii–Schiff and Jimbo–Miwa equations. The main objective of this study was to obtain novel resonant multi-soliton solutions and investigate inelastic interactions of traveling waves for the above-mentioned equation. Novel resonant multi-soliton solutions along with their essential conditions were obtained by using simplified LSP, and the conditions guaranteed the existence of resonant solitons. Furthermore, the obtained solutions were used to investigate the dynamic and fission behavior of Y-type multi-soliton waves. For an accurate investigation of physical phenomena, appropriate free parameters were chosen to ascertain the impact on the speed of traveling waves and the initiation time of fission. Three-dimensional and contour plots of the obtained solutions are presented in <xref ref-type="fig" rid="Figure1">Figures 1</xref>–<xref ref-type="fig" rid="Figure6">6</xref>. Additionally, two nonlinear equations were formulated and investigated using VR, and the related soliton molecules were simultaneously extracted. The reported resonant Y-type multi-soliton waves and equations are new and have not been previously investigated. They can be used to explain modeled physical phenomena and can provide information about dynamic behavior of shallow water waves.</p> </abstract>

A fourth-order nonlinear equation studied by using amultivariate bilinear neural network method

“…the interaction solution between lump, periodic wave, and 1-kink soliton can be obtained for Eq. (16).…”

“…where γ, λ and δ i (i = 1, 2, • • • , 5) is arbitrary constant, Kuo et al have recently completed this study of resonant Y-type multi-soliton solutions and soliton molecules for equation (1) by means of the Hirota bilinear method [16]. Ma has given a typical lump solutions of equation ( 1) [15].…”

Resonant Y-Type solutions, N-Lump waves, and hybrid solutions to a Ma-type model: a study of lump wave trajectories in superposition

“…which is then used to obtain the bilinear form for equation 4. This bilinear form is reported in reference [26] as follows:…”

“…which M i,j and D i,j are obtained by replacing k 1 and p 1 with k i and p i , respectively and k 2 and p 2 with k j and p j , respectively in the phase shift (26).…”