Bifurcation Analysis and Single Traveling Wave Solutions of the Variable-Coefficient Davey–Stewartson System

This paper mainly studies the bifurcation and single traveling wave solutions of the variable-coefficient Davey–Stewartson system. By employing the traveling wave transformation, the variable-coefficient Davey–Stewartson system is reduced to two-dimensional nonlinear ordinary differential equations. On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. On the other hand, we use the polynomial complete discriminant method to obtain the exact traveling wave solution of the variable-coefficient Davey–Stewartson system.

Novel Particular Solutions, Breathers, and Rogue Waves for an Integrable Nonlocal Derivative Nonlinear Schrödinger Equation

A determinant representation of the n -fold Darboux transformation for the integrable nonlocal derivative nonlinear Schödinger (DNLS) equation is presented. Using the proposed Darboux transformation, we construct some particular solutions from zero seed, which have not been reported so far for locally integrable systems. We also obtain explicit breathers from a nonzero seed with constant amplitude, deduce the corresponding extended Taylor expansion, and obtain several first-order rogue wave solutions. Our results reveal several interesting phenomena which differ from those emerging from the classical DNLS equation.

Multi and breather wave soliton solutions and the linear superposition principle for generalized Hietarinta equation

In this paper, we study the generalized ([Formula: see text])-dimensional Hietarinta equation which is investigated by utilizing Hirota’s bilinear method. Also, the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, multi-wave and breather wave solutions of the addressed equation with specific coefficients are presented. Finally, under certain conditions, the asymptotic behavior of solutions is analyzed in both methods. Moreover, we employ the linear superposition principle to determine [Formula: see text]-soliton wave solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation.

Nonlinear dynamical wave structures to the Zoomeron equation for population models

In this paper, the nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achevied for the first time in the framwork of the Paul-Painlevé approachmethod (PPAM). When the variables appearing in the exact solutions take specific values, the solaitry wave solutions will be easily satisfied.The realized results prove the efficiency of this technique.